Data Science Certificate Notes

Course 1 The Data Scientist’s Toolbox

This is my notebook for Coursera’s data science specialization certificate.

Week 1.1 Data Science in general

What is data science?

Data Science: Using data to answer question.

Data scientist: A data scientist is somebody who uses data to answer questions. A data scientist is somebody who combines the skills of software programmer, statistician and storyteller slash artist to extract the nuggets of gold hidden under mountains of data.

Why do we need data science? We have rich data and tools to analyses real world questions.

What is big data? There are a few qualities that characterize big data: Volume: huge amount of data Velocity: data is being generated and collected very fast Variety: The data we can analyse comes in many forms.

Data Science skills? Substantive Expertise: We need to have enough expertise in the area Hacking skills: Computer programing skills: cleaning and formatting Math & Statistics Knowledge: Analyze.

What is data? Wikipedia: A set of values of qualitative or quantitative variables. Measurements on a set of items.

We examined different sources of data that you may encounter, and emphasized the lack of tidy datasets. Examples of messy datasets, where raw data needs to be wrangled into an interpretable form, can include sequencing data, census data, electronic medical records, etc.

And finally, we return to our beliefs on the relationship between data and your question and emphasize the importance of question-first strategies. You could have all the data you could ever hope for, but if you don’t have a question to start, the data is useless.

Getting help Eric Raymond’s “How to ask questions the smart way”

The Data Science Process Every Data Science Project starts with a question that is to be answered with data. That means that forming the question is an important first step in the process. The second step is finding or generating the data you’re going to use to answer that question. With the question solidified and data in hand, the data are then analyzed, first by exploring the data and then often by modeling the data, which means using some statistical or machine learning techniques to analyze the data and answer your question. After drawing conclusions from this analysis, the project has to be communicated to others. Sometimes this is a report you send to your boss or team at work. Other times it’s a blog post. Often it’s a presentation to a group of colleagues. Regardless, a data science project almost always involves some form of communication of the projects’ findings. We’ll walk through these steps using a data science project example below.

Some cool data science projects: • Text analysis of Trump’s tweets confirms he writes only the (angrier) Android half, by David Robinson • Where to Live in the US, by Maelle Salmon • Sexual Health Clinics in Toronto, by Sharla Gelfand • “Hilary: the most poisoned baby name in US history”

Week 1.2 R software

Installing R: R is both a programming language and an environment. How to download R.

Installing R studio What is RStudio? RStudio is a graphical user interface for R, that allows you to write, edit and store code, generate, view and store plots, manage files, objects and dataframes, and integrate with version control systems – to name a few of its functions.

R packages There is a great website, RDocumentation, which is a search engine for packages and functions from CRAN, BioConductor, and GitHub (ie: the big three repositories) Installing from GitHub This is a more specific case that you probably won’t run into too often. In the event you want to do this, you first must find the package you want on GitHub and take note of both the package name AND the author of the package. Check out this guide for installing from GitHub, but the general workflow is: 1. install.packages(“devtools”) - only run this if you don’t already have devtools installed. If you’ve been following along with this lesson, you may have installed it when we were practicing installations using the R console 2. library(devtools) - more on what this command is doing immediately below this 3. install_github(“author/package”) replacing “author” and “package” with their GitHub username and the name of the package. Updating packages You can check what packages need an update with a call to the function old.packages() This will identify all packages that have been updated since you installed them/last updated them. To update all packages, use update.packages(). If you only want to update a specific package, just use once again install.packages(“packagename”) Unloading packages Sometimes you want to unload a package in the middle of a script - the package you have loaded may not play nicely with another package you want to use. To unload a given package you can use the detach() function. For example, detach(“package:ggplot2”, unload=TRUE) would unload the ggplot2 package (that we loaded earlier). Within the RStudio interface, in the Packages tab, you can simply unload a package by unchecking the box beside the package name. Uninstalling packages If you no longer want to have a package installed, you can simply uninstall it using the function remove.packages(). For example, remove.packages(“ggplot2”)

Use vignettes to learn examples of the related packages. If you still have questions about what functions within a package are right for you or how to use them, many packages include “vignettes.” These are extended help files, that include an overview of the package and its functions, but often they go the extra mile and include detailed examples of how to use the functions in plain words that you can follow along with to see how to use the package. To see the vignettes included in a package, you can use the browseVignettes() function. For example, let’s look at the vignettes included in ggplot2:browseVignettes(“ggplot2”) . You should see that there are two included vignettes: “Extending ggplot2” and “Aesthetic specifications.” Exploring the Aesthetic specifications vignette is a great example of how vignettes can be helpful, clear instructions on how to use the included functions.

Week 1.3 Version Control

Version Control Version control systems help to solve this problem by keeping a single, updated version of each file, with a record of all previous versions AND a record of exactly what changed between the versions. Git is a free and open source version control system Github is a cloud-based management system for your verision controlled files. Version control vocabulary There is a lot of vocabulary involved in working with Git, and often the understanding of one word relies on your understanding of a different Git concept. Take some time to familiarize yourself with the words below and read over it a few times to see how the concepts relate. Repository: Equivalent to the project’s folder/directory - all of your version controlled files (and the recorded changes) are located in a repository. This is often shortened to repo. Repositories are what are hosted on GitHub and through this interface you can either keep your repositories private and share them with select collaborators, or you can make them public - anybody can see your files and their history. Commit: To commit is to save your edits and the changes made. A commit is like a snapshot of your files: Git compares the previous version of all of your files in the repo to the current version and identifies those that have changed since then. Those that have not changed, it maintains that previously stored file, untouched. Those that have changed, it compares the files, logs the changes and uploads the new version of your file. We’ll touch on this in the next section, but when you commit a file, typically you accompany that file change with a little note about what you changed and why. When we talk about version control systems, commits are at the heart of them. If you find a mistake, you revert your files to a previous commit. If you want to see what has changed in a file over time, you compare the commits and look at the messages to see why and who. Push: Updating the repository with your edits. Since Git involves making changes locally, you need to be able to share your changes with the common, online repository. Pushing is sending those committed changes to that repository, so now everybody has access to your edits. Pull: Updating your local version of the repository to the current version, since others may have edited in the meanwhile. Because the shared repository is hosted online and any of your collaborators (or even yourself on a different computer!) could have made changes to the files and then pushed them to the shared repository, you are behind the times! The files you have locally on your computer may be outdated, so you pull to check if you are up to date with the main repository. Staging: The act of preparing a file for a commit. For example, if since your last commit you have edited three files for completely different reasons, you don’t want to commit all of the changes in one go; your message on why you are making the commit and what has changed will be complicated since three files have been changed for different reasons. So instead, you can stage just one of the files and prepare it for committing. Once you’ve committed that file, you can stage the second file and commit it. And so on. Staging allows you to separate out file changes into separate commits. Very helpful!

To summarize these commonly used terms so far and to test whether you’ve got the hang of this, files are hosted in a repository that is shared online with collaborators. You pull the repository’s contents so that you have a local copy of the files that you can edit. Once you are happy with your changes to a file, you stage the file and then commit it. You push this commit to the shared repository. This uploads your new file and all of the changes and is accompanied by a message explaining what changed, why and by whom.

Github and Git Install git and configure it for the use with Github, in preparation for linking it with RStudio.

Linking Git/GitHub and RStudio Not work for my mac. I just downloaded the git app to the mac. The terminal way is very bad.

Week 1.4 Misc.

Types of Data Science Questions

• Descriptive
  • The goal of descriptive analysis is to describe or summarize a set of data.
    • common descriptive statistics: measures of central tendency (eg: mean, median, mode) or measures of variability (eg: range, standard deviations or variance).
• Exploratory
  • The goal of exploratory analysis is to examine or explore the data and find relationships that weren’t previously known. (correlation)
• Inferential
  • The goal of inferential analyses is to use a relatively small sample of data to infer or say something about the population at large. (correlation)
• Predictive
  • The goal of predictive analysis is to use current data to make predictions about future data.
• Causal
  • looking at the cause and effect of a relationship.
• Mechanistic
  • understand the exact changes in variables that lead to exact changes in other variables.

Experimental Design

As a data scientist, you are a scientist and as such, need to have the ability to design proper experiments to best answer your data science questions!

What does experimental design mean?

Experimental design is organizing an experiment so that you have the correct data (and enough of it!) to clearly and effectively answer your data science question.

Some terms: * dependent variables, * independet variables, * confounder. + an extraneous variable that may affect the relationship between the dependent and independent variables.

p-heck

p-value. This is a value that tells you the probability that the results of your experiment were observed by chance

What is a p-value

Big Data

What is big data?

three qualities that are commonly attributed to big data sets: Volume, Velocity, Variety. From these three adjectives, we can see that big data involves large data sets of diverse data types that are being generated very rapidly.

# # The Data Scientist's Toolbox
# ###########
# # Week 1
# ###########
# # create a matrix
# example <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8), nrow = 4, ncol = 2)
# 
# # install packages
# # 1. install from CRAN
# # install.packages(c("ggplot2","devtools","lme4"))
# 
# # 2. Installing from Bioconductor (another repository)
# # source("https://bioconductor.org/biocLite.R")
# # This makes the main install function of BioConductor, biocLite(), available to you. Following this, you call the package you want to install in quotes, between the parentheses of the biocLite command, like so: biocLite("GenomicFeatures")
# # BiocLite()
# # BiocLite("GenomicFeatures")
# 
# # know the version and session info:
# version
# sessionInfo()
# 
# browseVignettes("ggplot2")
# 
# ###########
# # Week 4
# ###########
# 
# # R markdown
# 
# install.packages("rmarkdown")
# tinytex::install_tinytex()
# 
# 
# # install book down package
# install.packages("bookdown")

Course 2 R Programming

Week 2.1 R-Basics.

R is have five data type: vector, matrcies,list,factor,dataframe. R have five class: numeric, integer, complex,character, logical. R object can have attributes:dimension, length, class,name.

R data type

R have five basic or “atomic” classes of objects: * character * numeric(real numbers) * integer * complex * logical (True/False)

The most basic object is a vector. A vector can only contain objects of the same class

A list can contain objects of different classes.

Attributes

R objects can have attributes * names, dimnames * dimensions (e.g. matrices, arrays) * class * length * other user-defined attributes/metadata

Attributes of an object can be accessed using the attributes() function

Data Structure

Vector: Vectors are the most basic R data objects and there are five types of atomic vectors. They are logical, integer, numeric, complex, character. List: Lists are a special type of vector that can contain elements of different classes. Matrices:Matrices are vectors with a dimension attribute. Arrary can have more than two dimensions. Factor: Factors are used to represent categorical data. Data frame: They are represented as a special type of list where every element of the list have the same length.

Data Structure - Vectors

Vectors are the most basic R data objects and there are five types of atomic vectors. They are logical, integer, numeric, complex, character. The c() function can be used to create vectors of objects.

x <-c(0.5, 0.6)  ## numeric
x <-c(T,T)       ## logical
x <-c("a","b","c") ## character
x <- 9:29        ## integer
x <-c(1+0i,2+4i) ## complex

Using the vector() function, by default it will intialize the vector value.

x <-vector("numeric",length=10)
x

##  [1] 0 0 0 0 0 0 0 0 0 0

Implicit Coercion (Mixing Objects)

What if you create a vector containing different class of objects. When different objects are mixed in a vector, coercion occurs so that every element in the vector is of the same class.

y <-c(1.7,"a")   # numeric and character = character
class(y)        

## [1] "character"

y <-c(T,2)       # logical and numeric = numeric
class(y)

## [1] "numeric"

y<-c("a",T)      # character and logical = character
class(y)

## [1] "character"

# character less common than logical, logical less common than numeric.

So what happens if you take a vect you create a vector and you mix two different types of objects and so the general it that is that r. Will kind of create the least common denominator vector so, will not give you an error but what will happen is that it will coerce the vector to be the, the class that’s kind of the least common denominator. So here, in the first example, I’ve got in trouble concatenating number 1.7 and letter a, so clearly these are not in the same class one is numeric, and the other is character. So the least common denominator here, is going to be character. And so we’re, so what you’re going to get is that y is going to be a character vector, where the first element is going to be the string 1.7 and the second element’s going to be the, the letter A so in the second example here, I’ve got concatenating true, which is a logical, and a two, which is numeric.

Explicit Coercion

Objects can be explicitly coerced from one class to another using the as.* functions, if available.

x <-0:6
class(x)

## [1] "integer"

as.numeric(x)

## [1] 0 1 2 3 4 5 6

as.logical(x)

## [1] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE

as.character(x)

## [1] "0" "1" "2" "3" "4" "5" "6"

Nonsensical coercion results in NAs.

x <-c("a","b","c")
as.numeric(x)

## Warning: NAs introduced by coercion

## [1] NA NA NA

as.logical(x)

## [1] NA NA NA

as.complex(x)

## Warning: NAs introduced by coercion

## [1] NA NA NA

Data Structure - Lists

Lists are a special type of vector that can contain elements of different classes. Lists are a very important data type in R and you should get to know them well.

x <- list(1,"a",T,1+4i)
x

## [[1]]
## [1] 1
## 
## [[2]]
## [1] "a"
## 
## [[3]]
## [1] TRUE
## 
## [[4]]
## [1] 1+4i

So you can see that in the double brackets here so the, the elements are indexed by double brackets so the first element is the vector 1. The second element is a vector with A. The third element is a vector with true and the fourth element is a vector. With the complex number 1 + (4i). So lists are indexed you’ll notice that el, elements of a list will have double brackets around them elements of other vectors just have the single brackets, so that’s one way to separate a list from other types of vectors

Data Structure - Matrices

Matrices are vectors with a dimension attribute. The dimension attribute is itself an integer vector of length 2 (nrow,ncol).

m <-matrix(nrow =2,ncol=3)
m

##      [,1] [,2] [,3]
## [1,]   NA   NA   NA
## [2,]   NA   NA   NA

dim(m)

## [1] 2 3

attributes(m)

## $dim
## [1] 2 3

Matrices are constructed column-wise, so entries can be thought of starting in the “upper left” corner and running down the columns.

m <- matrix(1:6, nrow=2,ncol=3)
m

##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

Matrices can also be created directly from vectors by adding a dimension attribute.

m <- 1:10
m

##  [1]  1  2  3  4  5  6  7  8  9 10

dim(m) <- c(2,5)
m

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    3    5    7    9
## [2,]    2    4    6    8   10

Matrices can be created by column-bingding or row-binding with cbind() and rbind()

x <- 1:3
y <- 10:12
cbind(x,y)

##      x  y
## [1,] 1 10
## [2,] 2 11
## [3,] 3 12

rbind(x,y)

##   [,1] [,2] [,3]
## x    1    2    3
## y   10   11   12

Data Structure - Factors

Factors are used to represent categorical data. Factors can be unordered or ordered. One can think of a factor as an integer vector where each integer has a label. * Factors are treated specially by modelling functions like lm() and glm() * Using factors with labels is better than using integers because factors are self-describing; having a variable that has values “male” and “female’ is better than a variables that has values 1 and 2.

x <- factor(c("yes","yes","no","yes","no"))
x

## [1] yes yes no  yes no 
## Levels: no yes

table(x)

## x
##  no yes 
##   2   3

unclass(x) # show how R coded the factor

## [1] 2 2 1 2 1
## attr(,"levels")
## [1] "no"  "yes"

attr(x,"levels")

## [1] "no"  "yes"

The order of the levels can be set using the levels argument to factor(). This can be important in linear modelling because the first level is used as the baseline level.

x <- factor(c("yes","yes","no","yes","no"),levels=c("yes","no"))
x

## [1] yes yes no  yes no 
## Levels: yes no

table(x)

## x
## yes  no 
##   3   2

unclass(x) # show how R coded the factor

## [1] 1 1 2 1 2
## attr(,"levels")
## [1] "yes" "no"

attr(x,"levels")

## [1] "yes" "no"

Data Structure - Data Frames

Data Frames are used to store tabular data * They are represented as a special type of list where every element of the list have the same length. * unlike matrices, data frames can store different classes of objects in each column. Matrices must have every element be the same class. * Data frames also have a speecial attribute called row.names * can be converted to a matrix by calling data.matrix()

Subsetting

Subsetting - Basics

There are a number of operators that can be used to extract subsets of R objects. * [always returns an object of the same class as the orignial; can be used to select more than one element. * [[ is used to extract elements of a list or a data frame; it can only be used to extract a single element and the class of the returned object will not necessarily be a list of data frame. * $ is used to extract elements of a list or data frame by name; semantics are similar to [.

x <- c("a","b","c","c","d","a")
x[1]

## [1] "a"

x[2]

## [1] "b"

x[1:4]

## [1] "a" "b" "c" "c"

# subsetting using the name
x[x >"a"] #lexcical order

## [1] "b" "c" "c" "d"

u <-x >"a"
u

## [1] FALSE  TRUE  TRUE  TRUE  TRUE FALSE

Subsetting - Lists

# subsetting Lists
x <- list(foo =1:4, bar=0.6)
x

## $foo
## [1] 1 2 3 4
## 
## $bar
## [1] 0.6

x[1] # a list

## $foo
## [1] 1 2 3 4

x[[1]] # the sequence ; a vector

## [1] 1 2 3 4

x$bar 

## [1] 0.6

x[["bar"]]

## [1] 0.6

x["bar"]

## $bar
## [1] 0.6

# extract multiple element in a list
x <-list(foo=1:4, bar=0.6, baz="hello")
x[c(1,3)] # I want the first and the third element.

## $foo
## [1] 1 2 3 4
## 
## $baz
## [1] "hello"

The [[ operator can be used with computed indices; $ can only be used with literal names.

x <- list(foo=1:4, bar=0.6, baz="hello")
name <- "foo" # computed index for 'foo'
x[[name]] 

## [1] 1 2 3 4

x$name # element 'name' doesn't exist

## NULL

Subsetting Nested elements of a list. The [[ can take an integer sequence.

x <-list(a=list(10,12,14), b=c(3.14,2.81))
x[[c(1,3)]]

## [1] 14

x[[1]][[3]]

## [1] 14

x[[c(2,1)]]

## [1] 3.14

Subsetting - Matrices

matrices can be subsetted in the usual way with (i,j) type indices.

x <- matrix(1:6,2,3)
x[1,2]

## [1] 3

x[2,1]

## [1] 2

x[1,]

## [1] 1 3 5

x[,2]

## [1] 3 4

# By default, when a signle element of a matrix is retrieved, it is returned as a vector of length 1 rather than a 1*1 matrix. This behavior can be turned off by setting drop=F

x[1,2]

## [1] 3

x[1,2,drop=F] # always return element with same class.

##      [,1]
## [1,]    3

Subsetting - Partial Matching

# Partial matching of names is allowed with [[ and $
   x <- list(aardaark=1:5)  
x$a

## [1] 1 2 3 4 5

x[["a"]]

## NULL

x[["a", exact=F]]

## [1] 1 2 3 4 5

y <-list(aaax=1:5,aaab=6:9)
y$a

## NULL

Subsetting - Removing Missing Values

x <-c(1,2,NA)
x[!is.na(x)]

## [1] 1 2

# complete cases of very handy function which is when, when you have multiple sets of vectors or data, or large data frames or you want to subset all out, all the missing values.
x <- c(1,2,NA,4,NA,NA)
y <-c("a",NA,NA,"d",NA,"f")
good <- complete.cases(x,y)
good

## [1]  TRUE FALSE FALSE  TRUE FALSE FALSE

x[good] # x element where the related observation do not contains any missing value.

## [1] 1 4

y[good]

## [1] "a" "d"

# dataframe

airquality[1:6,]

##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 5    NA      NA 14.3   56     5   5
## 6    28      NA 14.9   66     5   6

good <- complete.cases(airquality)
airquality[good,][1:6,]

##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 7    23     299  8.6   65     5   7
## 8    19      99 13.8   59     5   8

# be caucious for the "".
x <- c(1,2,NA,4,NA,NA)
y <-c("a",NA,NA,"",NA,"f")
good <- complete.cases(x,y)
good

## [1]  TRUE FALSE FALSE  TRUE FALSE FALSE

x[good]

## [1] 1 4

Misc.

get working dirctory

# get working directory
getwd()

## [1] "/Users/wei/Documents/GitHub/Coursera_Data_Science_Certificate/Notebook"

# change working directory
setwd("~/Documents/GitHub/Coursera_Data_Science_Certificate")

R Console Input and Evaluation

“<-” symbol is the assignment operator. Assign a value to a symbol

x <-1

# two way to print the x
print(x)

## [1] 1

x

## [1] 1

msg <- "hello"
print(msg)

## [1] "hello"

Numbers

Numbers in R a generally treated as numeric objects (i.e. double precision real numbers)

If you explicitly want an integer, you need to specify the L suffix

Ex: Entering 1 gives you a numeric object; entering 1L explicitly gives you an integer.

There is also a special number Inf which represents infinity; e.g. 1/0; Inf can be used in ordinary calculations; e.g. 1/Inf is 0

1/Inf

## [1] 0

The value NaN represents an undefined values (” not a number); e.g 0/0 NaN can also be thought of as a missing value.

0/0

## [1] NaN

Missing Values

Missing values are denoted by NA or NaN for undefined athematical operations. * is.na() is used to test objects if they are NA * is.nan() is usest to test for NaN * Na values have a class also, so there are integer NA, character NA, etc. * A NAN value is also NA but the converse is not true. * “” is not na

x <-data.frame(foo=1:4,bar=c(T,T,F,F))
x

##   foo   bar
## 1   1  TRUE
## 2   2  TRUE
## 3   3 FALSE
## 4   4 FALSE

nrow(x)

## [1] 4

ncol(x)

## [1] 2

x <- c(1,2,NA,10,3)
is.na(x)

## [1] FALSE FALSE  TRUE FALSE FALSE

is.nan(x)

## [1] FALSE FALSE FALSE FALSE FALSE

x<-c(1,2,NaN,NA,4)
is.na(x)

## [1] FALSE FALSE  TRUE  TRUE FALSE

is.nan(x)

## [1] FALSE FALSE  TRUE FALSE FALSE

x <-c("a","","b")
is.na(x)

## [1] FALSE FALSE FALSE

x <-replace(x,x=="",NA)
is.na(x)

## [1] FALSE  TRUE FALSE

booklist related to R

A list of books related to R

Name Attribute

R objects can also have names, which is very useful for writing readable code and self-describing objects.

x <- 1:3
names(x)

## NULL

names(x) <- c("foo","bar","norf")

names(x)

## [1] "foo"  "bar"  "norf"

List can also have names.

x <-list(a=1,b=2,c=3)
x

## $a
## [1] 1
## 
## $b
## [1] 2
## 
## $c
## [1] 3

matrices can have names

m <- matrix(1:4, nrow =2 , ncol =2)
dimnames(m) <- list(c("a","b"), c("c","d"))
m

##   c d
## a 1 3
## b 2 4

Reading Data

• read.table, read.csv, for reading tabular data (for writing: write.table)
  • I would just add that the help page for read.table() says just as much under details read.csv and read.csv2 are identical to read.table except for the defaults. They are intended for reading ‘comma separated value’ files (‘.csv’) or (read.csv2) the variant used in countries that use a comma as decimal point and a semicolon as field separator.. So to the OP - yes, you would want read.table when your data don’t match the default values for read.csv
  • read.csv(file, header =T, stringsAsFactors = T) [by default, strings are automotically convert to factor]
• readLines, for reading lines of a text file (for writing: writeLines) +read.csv is identical is identical to read.table except that the default separator is a comma.
• source, for reading in R code files (inverse of dump)
• dget, for reading in R code files (inverse of dput)
• load, for reading in saved workspaces (inverse of save)
• unserialize, for reading single R objects in binary form (inverse of serialize)

Read in larger datasets with read.table

• Use the colClasses argument. Specifiying htis option instaed ousing the default can make read.table run MUCH faster, oten twice as fast. In order to use this option, you have to know the class of each column in your data frame. If all the columns are “numeric”, for example, then you can just set colClasses = “numeric”. A quick and dirty way to figure out the classes of each column is the following:

# initial <- read.table("datatable.txt",nrows=100)
# classes <- sapply(initial, class)
# tabAll <- read.table("datatable.txt",colClasses =classes)

Textual Data Formats

The dput() is used to create a minimal reproducible example, when you have question that you would like to ask on the website, you need to prepare a minimal reprocuible example, so others can use that to reprocduce your error.

When you have quesitons, but your did not what to upload all the data, you can use this function to generate the minimal amount of data.

Interfaces to the Outside World

Data are read in using connection interfaces. Connections can be made to files (most common) or to other more exotic things.

• file, opens a connection to a file
• gzfile, opens a connection to a file compressed with gzip
• bzfile, opens a connection to a file compressed with bzip2
• url, opens a connection to a webpage

Cectorized Operations

Many operations in R are vectorized making code more efficient, concise, and easier to read.

x <- 1:4
y <- 6:9

x+y

## [1]  7  9 11 13

x >3

## [1] FALSE FALSE FALSE  TRUE

x*y

## [1]  6 14 24 36

# matrices

x <-matrix(1:4,2,2);y <- matrix(rep(10,4),2,2)

x*y

##      [,1] [,2]
## [1,]   10   30
## [2,]   20   40

x/y

##      [,1] [,2]
## [1,]  0.1  0.3
## [2,]  0.2  0.4

x %*% y ## true matrix multiplication

##      [,1] [,2]
## [1,]   40   40
## [2,]   60   60

Week 1 Quiz

# install dplyr package
# install.packages("dplyr")
 library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

# import the dataset
data1 <-read.csv("../Data/hw1_data.csv")

# get the class of each column
lapply(data1,class)

## $Ozone
## [1] "integer"
## 
## $Solar.R
## [1] "integer"
## 
## $Wind
## [1] "numeric"
## 
## $Temp
## [1] "integer"
## 
## $Month
## [1] "integer"
## 
## $Day
## [1] "integer"

# check the column names of the dataset
head(data1)

##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 5    NA      NA 14.3   56     5   5
## 6    28      NA 14.9   66     5   6

# Extract the first 2 rows of the data frame and print them to the console.
head(data1,n=2)

##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2

# Extract the last 2 rows 
tail(data1, n=2)

##     Ozone Solar.R Wind Temp Month Day
## 152    18     131  8.0   76     9  29
## 153    20     223 11.5   68     9  30

# the value of Ozone in the 47 row
data1[47,"Ozone"]

## [1] 21

# how many missing values
sum(is.na(data1$Ozone))

## [1] 37

# mean
mean(data1$Ozone,na.rm=T)

## [1] 42.12931

# Extract the subset of rows of the data frame where Ozone values are above 31 and Temp values are above 90. What is the mean of Solar.R in this subset?

data2 <- data1 %>%
  filter(Ozone>31 & Temp>90 & !is.na(Ozone) & !is.na(Temp))

mean(data2$Solar.R,na.rm=T)

## [1] 212.8

# What is the mean of "Temp" when "Month" is equal to 6? 

data3 <-data1 %>%
  filter(Month==6)

mean(data3$Temp,na.rm=T)

## [1] 79.1

# What was the maximum ozone value in the month of May (i.e. Month is equal to 5)?

data4 <-data1 %>%
  filter(Month==5)

max(data4$Ozone, na.rm=T)

## [1] 115

Week 2.2 Control Structures

Control structures in R allow you to control the flow of execution of the program, depending on runtime conditions. Common structures are

• is, else: testing a condition
• for: execute a loop a fixed number of times
• while: execute a loop while a condition is true
• repeat: execute an infinite loop
• break: break the execution of a loop
• next: skip and interation of a loop
• return: exit a function

control structures - if - else

age <- 20
if (age > 18){
  print ("Major")
} else {
  print ("Minor")
}

## [1] "Major"

#ifelse short sytax
age <- 20
ifelse(age>=18, "Major", "Minor")

## [1] "Major"

# nested ifelse
x <- 0

if (x<0){
  print ("negative")
} else if (x>0){
  print ("positive")
} else {
  print ("Zero")
}

## [1] "Zero"

#alternatively
x<-0
ifelse(x<0,"negative",ifelse(x==0,"Zero","positive"))

## [1] "Zero"

Control Structures - For Loops

x <- c("a","b","c","d")
for(i in 1:4){
  print(x[i])
}

## [1] "a"
## [1] "b"
## [1] "c"
## [1] "d"

for (i in seq_along(x)) {
  print(x[i])
}

## [1] "a"
## [1] "b"
## [1] "c"
## [1] "d"

for (letter in x) {
print(letter)
}

## [1] "a"
## [1] "b"
## [1] "c"
## [1] "d"

Nested for loops

x <- matrix(1:6, 2,3)

for (i in seq_len(nrow(x))) {
  for (j in seq_len(ncol(x))) {
    print(x[i,j])
  }
}

## [1] 1
## [1] 3
## [1] 5
## [1] 2
## [1] 4
## [1] 6

Be careful with nesting though. Nesting beyond 2-3 levels is often very difficult to read/understand

Control Structures - While loops

While loops begin by testing a condition. If it is true, then they execute the loop body. Once the loop body is execured, the condition is tested again, and so forth.

count <-0

while(count < 10){
  print(count)
  count <- count +1
}

## [1] 0
## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5
## [1] 6
## [1] 7
## [1] 8
## [1] 9

While if treated not properly, it may have infinite loop, use for loop instead of while loop.

Control Structures - Repeat, Next, Break

Repeat intiate an infinite loop; these are not commonly used in statistical applications but they do have their uses. The only way to exit a repeat looop is to call break

# x0 <-1
# tol <- 1e-8

# repeat{
#   x1 <- computeEstimate()
#   
#   if(abs(x1-x0) < tol) {
#     break
#   } else{
#     x0 <- x1
#   }
#   }

The loop in the previous slide is a bit dangerous because there’s no guarantee it will stop. Better to set a hard limit on the number of iteration (e,g. using a for loop) and then report whether convergence was achieved or not.

next is used to skip an iteration of a loop

for (i in 1:100) {
  if(i <=20){
    ## skip the first 20 iterations
    next
  }
  ## do something here
}

“return” signals that a function should exit and return a given value

Control sturctures summary

• control sturcutes like if, while, and for allow you to control the flow of an R program
• infinite loops hsould generally be avoided, even if they are theoretically correct.
• control sturctures mentioned here are primarily useful for writing programs; for commend-line interatice work, the * apply functions are more useful.

R funcitons.

# add two number
add2 <- function(x,y) {
  x + y
}

add2(3,4)

## [1] 7

# take a vector number and return the number bigher than 10.

above10 <- function(x){
  use <- x > 10
  x[use]
}

# take a vector number and return the number bigher than a number.
above <-function(x,n){
  use <- x>n # logical statement
  x[use]
}

x <-1:20

above(x,3)

##  [1]  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20

# set up a default number

above <-function(x,n=10){
  use <- x>n # logical statement
  x[use]
}

x <-1:20

above(x)

##  [1] 11 12 13 14 15 16 17 18 19 20

above(x,5)

##  [1]  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20

# calculate the mean of each vector

columnmean <- function(y, removeNA=TRUE){
  nc <- ncol(y)
  means <- numeric(nc) # a vecctor with zero entry.
  for (i in 1:nc) {
    means[i] <- mean(y[,i], na.rm=removeNA)
  }
  means
}

x <- matrix(1:18,2,9)
columnmean(x)

## [1]  1.5  3.5  5.5  7.5  9.5 11.5 13.5 15.5 17.5

columnmean(airquality)

## [1]  42.129310 185.931507   9.957516  77.882353   6.993464  15.803922

columnmean(airquality,FALSE)

## [1]        NA        NA  9.957516 77.882353  6.993464 15.803922

The … argument indicate a variable number of arguments that are usually passed on to other functions.

myplot <- function(x,y,type="1",...) {
  plot(x,y,type=type,...)
}

Scoping rules

search() # give searh path for R objects, give a list of attached packages and R objects, usually data.frames.

##  [1] ".GlobalEnv"        "package:dplyr"     "package:stats"    
##  [4] "package:graphics"  "package:grDevices" "package:utils"    
##  [7] "package:datasets"  "package:methods"   "Autoloads"        
## [10] "package:base"

Lexical scoping

f <- function(x,y){
  x^2 + y/z
}

z <- 3
f(4,2)

## [1] 16.66667

# z is a free variable.

Environment is a collection of (symbo,value) pairs.

make a function inside another function

scoping rule, define a lm() function, why it does not recoganize it as a part of stat package, because r have a coping rule.it search is first found in the environment in which a function was defined, then search for it in the parent environment, then search for it until the golobal environment, thencontinue down the search list until we hit the empty environment

make.power <- function(n) {
  pow <- function(x){
    x^n
  }
  pow
}

cube <- make.power(3)
suqre <- make.power(2)
cube(3)

## [1] 27

suqre(3)

## [1] 9

# what's in a function's environment?
ls(environment(cube))

## [1] "n"   "pow"

```{r} y <- 10

f <- function(x){ y <-2 y^2 + g(x) }

  g <- function(x){
    x*y
  }

f(3)

with lexical scoping the value of y in the function g is looked up in the environment in which the funciton was defined, in this case the global environment, so the value of y is 10.

coding standard of R programing

• always use text files/ text editor ident your code, 8 spaces is idea limit the width of your code (80 columns?)
• limit the length of indivuidual funcitons

Dates and Times

R has developed a special representation of dates and times * Dates are represented by the Date class * Times are represented by the POSIXct or the POSIXLt clas * Date are stored internally as the number of days since 1970=01-01 * TImes are stored internally as the number of seconds since 1970=01-01

Dates in R Dates are represend by the date class and can be coerced from a character string using the as.Date() funciton.

x <-as.Date("1970-01-01")
x

## [1] "1970-01-01"

y <- as.Date("1993-11-18")

unclass(x)

## [1] 0

unclass(y) # how many days from 1970-01-01 untill 1993-11-18

## [1] 8722

Times are represented using the POSIcct or pOSiclt class * POSIXct is juest a very large integer under the hood; it uses a useful class when you want to store timesi n someting like a data frame.

• posixlt is a list underneath and it stores a buch of other useful information like the day of the week, day of the year, month, day of the month.

There are number of generic functions that work on dates and times;

• weekdays: give the day of the week
• months:give the month name
• quarters: give the quarter number (“Q1”, “Q2”,“Q3”, or “Q4”)

Times can be coerced from a character string using the as.POSIXlt or as.POSIXct fucntion.

x <- Sys.time()
x

## [1] "2022-12-12 15:14:53 EST"

p <- as.POSIXlt(x)
p

## [1] "2022-12-12 15:14:53 EST"

class(x)

## [1] "POSIXct" "POSIXt"

class(p)

## [1] "POSIXlt" "POSIXt"

unclass(p)

## $sec
## [1] 53.24007
## 
## $min
## [1] 14
## 
## $hour
## [1] 15
## 
## $mday
## [1] 12
## 
## $mon
## [1] 11
## 
## $year
## [1] 122
## 
## $wday
## [1] 1
## 
## $yday
## [1] 345
## 
## $isdst
## [1] 0
## 
## $zone
## [1] "EST"
## 
## $gmtoff
## [1] -18000
## 
## attr(,"tzone")
## [1] ""    "EST" "EDT"

names(unclass(p))

##  [1] "sec"    "min"    "hour"   "mday"   "mon"    "year"   "wday"   "yday"  
##  [9] "isdst"  "zone"   "gmtoff"

p$sec

## [1] 53.24007

Finally, there is the strptime funciton in case your dates are written in a different format

datestring <- c("January 10, 2012 10:40", "December 9, 2011 9:10")
x <-strptime(datestring, "%B %d,%Y %H:%M")
x

## [1] "2012-01-10 10:40:00 EST" "2011-12-09 09:10:00 EST"

class(x)

## [1] "POSIXlt" "POSIXt"

You can use mathematical operations on dates and times. Well, really just + and -, you can do comparisons too (oe. ==, <=)

# x <- as.Date("2012-01-01")
# class(x)
# y <- strptime("9 Jan 2011 11:34:21", "%d %b %Y %J:%M:%S")
# z <- strptime("9 Jan 2011", "%d %b %Y")
# class(y)
# 
# x-y
# x-z
# x <- as.POSIXlt(x)
# x-y
# x-z
# 
# 
# n <- as.Date("9 Jan 2011", "%d %b %Y")
# x <- as.Date("2012-01-01")
# x-n

Even keeps track of leap years, leap seconds, daylight savings, and time zones.

x <-as.Date("2012-03-01")
y <-as.Date("2012-02-28")

x-y

## Time difference of 2 days

x <-as.POSIXct("2012-10-25 01:00:00")
y <- as.POSIXct("2012-10-25 06:00:00", tz="GMT") # change time zone
y-x

## Time difference of 1 hours

summary * dates and times have special classes in R that allow for numerical and statistical calculations * dates use the date class * ITme use the POSIXct and POSIXlt class * character strings can be coerced to Date/Time classes using the strptyime function or the as.Date, as.POSIXlt, or as.POSIXct.

Programming Assignment 1: Quiz

A good reference

# # Write a function named 'pollutantmean' that calculates the mean of a pollutant (sulfate or nitrate) across a specified list of monitors. The function 'pollutantmean' takes three arguments: 'directory', 'pollutant', and 'id'. Given a vector monitor ID numbers, 'pollutantmean' reads that monitors' particulate matter data from the directory specified in the 'directory' argument and returns the mean of the pollutant across all of the monitors, ignoring any missing values coded as NA. A prototype of the function is as follows
# 
# getwd()
# 
# pollutantmean <- function(directory,pollutant, id=1:332) {
#   
#   full <- NA
#   
#   for (x in id){
#   path <- paste("./","data/",directory,"/",sprintf("%.3d",x),".csv",sep="")
#   rcsv <- read.csv(path)
#   full<-rbind(full,rcsv)
#   }
#   
#   x<-mean(full[,pollutant],na.rm=T)
#   x
# }
# 
# # Test
# pollutantmean("specdata","nitrate", 70:72)
# pollutantmean("specdata","nitrate", 23)
# 
# # save the above as a function
# 
# 
# # Write a function that reads a directory full of files and reports the number of completely observed cases in each data file. The function should return a data frame where the first column is the name of the file and the second column is the number of complete cases. A prototype of this function follows
# 
# 
# # library(dplyr)
# # complete <- function(directory, id=1:332){
# #   
# #    full <-NA
# #    
# #    for (x in id){
# #                 path <- paste("./","data/",directory,"/",sprintf("%.3d",x),".csv",sep="")
# #                 rcsv <- read.csv(path)
# #                 full<-rbind(full,rcsv)
# #    }
# #    
# #    results <-full %>% 
# #                  mutate(a=case_when(((!is.na(sulfate))&(!is.na(nitrate)))~1,TRUE~0)) %>%
# #                  group_by(ID) %>%
# #                  mutate(nobs=sum(a)) %>%
# #                  filter(row_number()==1 & !is.na(ID)) %>%
# #                  ungroup() %>%
# #                  select(ID,nobs) 
# #    results<-as.data.frame(results)
# #    results
# # }
# # 
# # 
# # 
# # xx<-complete("specdata",30:25)
# # x<-complete("specdata",3)
# # 
# # # Write a function that takes a directory of data files and a threshold for complete cases and calculates the correlation between sulfate and nitrate for monitor locations where the number of completely observed cases (on all variables) is greater than the threshold. The function should return a vector of correlations for the monitors that meet the threshold requirement. If no monitors meet the threshold requirement, then the function should return a numeric vector of length 0. A prototype of this function follows.
# # 
# # source("./2_R Programming/complete.R")
# # corr <- function(directory, threshold=0){
# #    
# #    for (x in 1:332){
# #                 path <- paste("./","data/",directory,"/",sprintf("%.3d",x),".csv",sep="")
# #                 rcsv <- read.csv(path)
# #                 full<-rbind(full,rcsv)
# #    }
# #    
# #    nobs <- complete(directory)
# #    
# #    full_nobs <- left_join(full,nobs, by="ID")
# #    
# #    results <-    full_nobs %>%
# #                  group_by(ID) %>%
# #                  mutate(correlation=cor(sulfate,nitrate,use="na.or.complete")) %>%
# #                  filter(row_number()==1) %>%
# #                  ungroup() %>%
# #                  select(ID,nobs,correlation) %>%
# #                  filter(nobs>threshold)
# # 
# #    vec <-results$correlation
# # }
# # 
# # 
# # cr<-corr("specdata")
# # 
# # summary(cr)
# # length(cr)
# # 
# # cr<-corr("specdata",5000)
# # summary(cr)
# 
# ```
# 
# QUIZ
# 
# ```{r}
# # # 1 might be faster
# # pollutantmean <- function(directory, pollutant, id = 1:332) {
# #     ## 'directory' is a character vector of length 1 indicating
# #     ## the location of the CSV files
# # 
# #     ## 'pollutant' is a character vector of length 1 indicating
# #     ## the name of  the pollutant for which we will calcultate the
# #     ## mean; either "sulfate" or "nitrate"
# # 
# #     ## 'id' is an integer vector indicating the monitor ID numbers
# #     ## to be used
# # 
# #     ## Return the mean of the pollutant across all monitors list
# #     ## in the 'id' vector (ignoring NA values)
# #     ## NOTE: Do not round the result
# #     means <- c()
# # 
# #     for(monitor in id){
# #         path <- paste(getwd(), "/", directory, "/", sprintf("%03d", monitor), ".csv", sep = "")
# #         monitor_data <- read.csv(path)
# #         interested_data <- monitor_data[pollutant]
# #         means <- c(means, interested_data[!is.na(interested_data)])
# #     }
# # 
# #     mean(means)
# # }
# # 
# # # 3 might be faster
# # corr <- function(directory, threshold = 0){
# #     ## 'directory' is a character vector of length 1 indicating
# #     ## the location of the CSV files
# # 
# #     ## 'threshold' is a numeric vector of length 1 indicating the
# #     ## number of completely observed observations (on all
# #     ## variables) requi?red to compute the correlation between
# #     ## nitrate and sulfate; the default is 0
# # 
# #     ## Return a numeric vector of correlations
# #     ## NOTE: Do not round the result!
# #     cor_results <- numeric(0)
# # 
# #     complete_cases <- complete(directory)
# #     complete_cases <- complete_cases[complete_cases$nobs>=threshold, ]
# #     #print(complete_cases["id"])
# #     #print(unlist(complete_cases["id"]))
# #     #print(complete_cases$id)
# # 
# #     if(nrow(complete_cases)>0){
# #         for(monitor in complete_cases$id){
# #             path <- paste(getwd(), "/", directory, "/", sprintf("%03d", monitor), ".csv", sep = "")
# #             #print(path)
# #             monitor_data <- read.csv(path)
# #             #print(monitor_data)
# #             interested_data <- monitor_data[(!is.na(monitor_data$sulfate)), ]
# #             interested_data <- interested_data[(!is.na(interested_data$nitrate)), ]
# #             sulfate_data <- interested_data["sulfate"]
# #             nitrate_data <- interested_data["nitrate"]
# #             cor_results <- c(cor_results, cor(sulfate_data, nitrate_data))
# #         }
# #     }
# #     cor_results
# # }
# 
# 
# source("./2_R Programming/pollutantmean.R")
# source("./2_R Programming/complete.R")
# source("./2_R Programming/corr.R")
# 
# pollutantmean("specdata", "sulfate", 1:10)
# pollutantmean("specdata", "nitrate", 70:72)
# pollutantmean("specdata", "sulfate", 34)
# pollutantmean("specdata", "nitrate")
# 
# cc <- complete("specdata", c(6, 10, 20, 34, 100, 200, 310))
# print(cc$nobs)
# 
# cc <- complete("specdata", 54)
# print(cc$nobs)
# 
# #2  FASTER musch better
# complete <- function(directory, id = 1:332){
#     ## 'director' is a character vector of length 1 indicating
#     ## the location of the CSV files
#     
#     ## 'id' is an integer vector indicating the monitor ID numbers
#     ## to be used
#     
#     ## Return a data frame of the from:
#     ## id nobs
#     ## 1  117
#     ## 2  1041
#     ## ...
#     ## where 'id' is the monitor ID number and 'nobs' is the
#     ## number of complete cases
#     results <- data.frame(id=numeric(0), nobs=numeric(0))
#     for(monitor in id){
#         path <- paste("./","data/",directory,"/",sprintf("%.3d",monitor),".csv",sep="")
#         monitor_data <- read.csv(path)
#         interested_data <- monitor_data[(!is.na(monitor_data$sulfate)), ]
#         interested_data <- interested_data[(!is.na(interested_data$nitrate)), ]
#         nobs <- nrow(interested_data)
#         results <- rbind(results, data.frame(id=monitor, nobs=nobs))
#     }
#     results
# }
# 
# RNGversion("3.5.1")  
# set.seed(42)
# cc <- complete("specdata", 332:1)
# use <- sample(332, 10)
# print(cc[use, "nobs"])
# 
# cr <- corr("specdata")                
# cr <- sort(cr)   
# RNGversion("3.5.1")
# set.seed(868)                
# out <- round(cr[sample(length(cr), 5)], 4)
# print(out)
# 
# cr <- corr("specdata", 129)                
# cr <- sort(cr)                
# n <- length(cr)    
# RNGversion("3.5.1")
# set.seed(197)                
# out <- c(n, round(cr[sample(n, 5)], 4))
# print(out)
# 
# cr <- corr("specdata", 2000)                
# n <- length(cr)                
# cr <- corr("specdata", 1000)                
# cr <- sort(cr)
# print(c(n, round(cr, 4)))
# 

Week 2.3 Loop Functions and Debugging

Loop function-lapply

• lapply: loop over a list and evaluate a function on each element
• sapply: same as lapply but try to simplify the result
• apply: apply a function over the margins of an array
• tapply: apply a function over subsets of a vector
• mapply: multivariate version of lapply

# lapply always returns a list , regardless of the class of the input

x <-list(a=1:5,b=rnorm(10))

lapply(x,mean)

## $a
## [1] 3
## 
## $b
## [1] -0.1866581

# anaymous function for extracting the first column of each matrix
x <-list(a=matrix(1:4, 2,2), b=matrix(1:6,3,2))
x

## $a
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
## 
## $b
##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

lapply(x,function(elt) elt[,1])

## $a
## [1] 1 2
## 
## $b
## [1] 1 2 3

sapply will try to simplify the result of lapply if possible. * if the result is a list where every element is length 1, then a vector is returned * if the result is a list where every eleemnent is a vector of the same length(>1), a matrix is returned. * if it can’t figure things out, a list is returend.

Loop Functions-apply

apply is used to evaluate a function (often an anonymous one) over the margins of an array. * if is most often used to apply a fucntion to the rows or columns of a matrix * if can be sued with general arrays,e.g. taking the average of an array of matrices * if is not really faster than writing a loop, but it works in one line!

array is a vector has dimension attached to it. a matrix is a two dimensional array.

x <-matrix(rnorm(200),20,10)

# 2 means pass the function to each column
apply(x,2,mean)

##  [1] -0.384887337  0.023777787 -0.006475793  0.572331367  0.061825351
##  [6] -0.088651818 -0.203253311 -0.334171373 -0.097099637  0.169676942

# 1 means pass the function to each row
apply(x,1,sum)

##  [1] -4.01136704  0.10485164 -2.58301846 -0.26681636  3.25832809  1.19363931
##  [7] -1.34421075  3.00278607 -4.88235967  0.05176391  1.92226815 -0.39258860
## [13]  4.75934813 -0.89500830 -0.66276031 -0.67738082  2.50753524  1.28942378
## [19] -4.42320688 -3.68978357

# For sums and means of matrix dimensions, we have some shortcuts.
 # rowSums=apply(x,1,sum)
 # rowMeans=apply(x,1,mean)
 # colSums=apply(x,2,sum)
 # colMeans=apply(x,2,mean)

x <-matrix(rnorm(200),20,10)
apply(x,1,quantile,probs=c(0.25,0.75)) # for each row, two line report

##           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
## 25% -0.5144582 -0.3008597 -0.3365292 -0.2666854 -0.6383236 -0.9676114
## 75%  1.0140023  0.9718227  0.8551695  0.9117487  0.2483074  0.5586648
##           [,7]       [,8]        [,9]      [,10]      [,11]      [,12]
## 25% -0.1144520 -0.5148152 -0.64149489 -0.8004039 -0.8000563 -0.8882266
## 75%  0.7066669  1.0640268  0.03036087  0.3528416  0.6511011  0.7170751
##           [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
## 25% -0.07590375 0.04013756 -0.2849336 -0.5192974 -0.9227459 -0.5394082
## 75%  0.85743312 1.12823153  0.4305149  0.6387993  0.7034466  1.4013457
##           [,19]      [,20]
## 25% -0.93388887 -0.7359109
## 75% -0.09296779  1.2690149

a <- array(rnorm(2*2*10),c(2,2,10))
a

## , , 1
## 
##          [,1]        [,2]
## [1,] 1.195492  0.26474392
## [2,] 0.193286 -0.03522272
## 
## , , 2
## 
##             [,1]       [,2]
## [1,] -0.52213407  0.8407511
## [2,]  0.03196943 -0.7653568
## 
## , , 3
## 
##           [,1]       [,2]
## [1,] 0.4612552  2.5687702
## [2,] 1.2869093 -0.4152069
## 
## , , 4
## 
##            [,1]      [,2]
## [1,] -0.8733966 0.6248820
## [2,] -1.2412370 0.5586125
## 
## , , 5
## 
##           [,1]       [,2]
## [1,] 0.1034446  0.7362299
## [2,] 0.3005623 -1.0792540
## 
## , , 6
## 
##            [,1]       [,2]
## [1,] -0.3903477 -0.3559669
## [2,]  0.5201381  0.4265609
## 
## , , 7
## 
##            [,1]       [,2]
## [1,]  0.4733110 -0.4957877
## [2,] -0.9362402 -0.3778814
## 
## , , 8
## 
##            [,1]      [,2]
## [1,] -1.1822617 -1.429960
## [2,]  0.8610738  0.479317
## 
## , , 9
## 
##           [,1]      [,2]
## [1,] -1.149511 0.2100223
## [2,]  1.893581 0.1828451
## 
## , , 10
## 
##           [,1]       [,2]
## [1,] -2.181171 -0.2729853
## [2,] -1.352447 -0.9145669

apply(a,c(1,2),mean) # collapse the third dimension.

##            [,1]       [,2]
## [1,] -0.4065319  0.2690700
## [2,]  0.1557596 -0.1940153

rowMeans(a, dims=2)

##            [,1]       [,2]
## [1,] -0.4065319  0.2690700
## [2,]  0.1557596 -0.1940153

Loop Functions-mapply

mapply is a multivariate apply of sorts which applies a function in parallel over a set of arguments.

# The following is tedious to type

list(rep(1,4),rep(2,3),rep(3,2),rep(4,1))

## [[1]]
## [1] 1 1 1 1
## 
## [[2]]
## [1] 2 2 2
## 
## [[3]]
## [1] 3 3
## 
## [[4]]
## [1] 4

# instead we can do

mapply(rep, 1:4,4:1)

## [[1]]
## [1] 1 1 1 1
## 
## [[2]]
## [1] 2 2 2
## 
## [[3]]
## [1] 3 3
## 
## [[4]]
## [1] 4

vectorizing a function

noise <- function(n,mean,sd) {
  rnorm(n,mean,sd)
}

mapply(noise,1:5,1:5,2)

## [[1]]
## [1] -0.2796253
## 
## [[2]]
## [1] -0.7715426  0.7128950
## 
## [[3]]
## [1] 5.4787806 2.3989167 0.5193307
## 
## [[4]]
## [1] 2.0902661 0.2739412 4.2054075 5.7972823
## 
## [[5]]
## [1] 3.402506 8.850193 5.224416 4.117203 7.300289

Loop Functions-tapply

tapply is used to apply a function over subsets of a vector.

# take group means
str(tapply)

## function (X, INDEX, FUN = NULL, ..., default = NA, simplify = TRUE)

# x is a vector
# index is a factor or a list of factors
# fun is a function to be applied
# simplify, should we simplify the results?

x <- c(rnorm(10),runif(10),rnorm(10,1))
x

##  [1] -1.9530536 -0.8890494 -0.5474696 -0.2920880  0.4328068 -0.7330734
##  [7]  0.7492089 -0.4357303 -0.4787891 -0.3521036  0.2119030  0.6541679
## [13]  0.1689355  0.4887188  0.2675069  0.9347861  0.9275142  0.6929194
## [19]  0.1925838  0.7886075  1.3176254 -0.9808342  1.1559721  1.6496613
## [25]  0.8158955  1.3689948  1.9398115  2.1256521  1.4118044  1.2484204

f <- gl(3,10) # generate factor level
f

##  [1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3
## Levels: 1 2 3

tapply(x,f,mean)

##          1          2          3 
## -0.4499341  0.5327643  1.2053003

tapply(x,f,mean, simplify=F)

## $`1`
## [1] -0.4499341
## 
## $`2`
## [1] 0.5327643
## 
## $`3`
## [1] 1.2053

tapply(x,f,range)

## $`1`
## [1] -1.9530536  0.7492089
## 
## $`2`
## [1] 0.1689355 0.9347861
## 
## $`3`
## [1] -0.9808342  2.1256521

Loop Funcitons- split

split takes a vector or other objects and splits it into groups determined by a factor or list of factors

str(split)

## function (x, f, drop = FALSE, ...)

# x is a vector (or) list or data frame
# f is a factor (or coerced to one) or a list of factors
# drop indicates whether empty factors levels should be dropped

x <- c(rnorm(10), runif(10), rnorm(10,1))

f <- gl(3,10)

split(x,f) # split always return a list back so you can use lapply or sapply

## $`1`
##  [1]  0.77191517  0.84172368  0.64496158 -0.06281806 -1.52460670  0.10031263
##  [7] -0.31408818  0.75974481 -0.92279417 -0.30064507
## 
## $`2`
##  [1] 0.11769696 0.18748257 0.95307847 0.74800326 0.20658687 0.46935286
##  [7] 0.09097327 0.08914456 0.16947099 0.59634110
## 
## $`3`
##  [1]  0.69647124 -0.77221595  1.09560620  1.55347742 -0.62729197  0.06046179
##  [7]  1.48082677  1.95200018  0.63581882 -0.05853180

# a common idiom is split followed by an lapply

# The following two are the same.
lapply(split(x,f),mean)

## $`1`
## [1] -0.000629431
## 
## $`2`
## [1] 0.3628131
## 
## $`3`
## [1] 0.6016623

tapply(x,f,mean,simplify=F)

## $`1`
## [1] -0.000629431
## 
## $`2`
## [1] 0.3628131
## 
## $`3`
## [1] 0.6016623

library(datasets)
head(airquality)

##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 5    NA      NA 14.3   56     5   5
## 6    28      NA 14.9   66     5   6

# calucualte the mean by group

# 1 first split the data frame into monthly pieces
s <- split(airquality, airquality$Month)
lapply(s, function(x) colMeans(x[,c("Ozone", "Solar.R", "Wind")]))

## $`5`
##    Ozone  Solar.R     Wind 
##       NA       NA 11.62258 
## 
## $`6`
##     Ozone   Solar.R      Wind 
##        NA 190.16667  10.26667 
## 
## $`7`
##      Ozone    Solar.R       Wind 
##         NA 216.483871   8.941935 
## 
## $`8`
##    Ozone  Solar.R     Wind 
##       NA       NA 8.793548 
## 
## $`9`
##    Ozone  Solar.R     Wind 
##       NA 167.4333  10.1800

sapply(s, function(x) colMeans(x[,c("Ozone", "Solar.R", "Wind")]))

##                5         6          7        8        9
## Ozone         NA        NA         NA       NA       NA
## Solar.R       NA 190.16667 216.483871       NA 167.4333
## Wind    11.62258  10.26667   8.941935 8.793548  10.1800

sapply(s, function(x) colMeans(x[,c("Ozone", "Solar.R", "Wind")],na.rm=T))

##                 5         6          7          8         9
## Ozone    23.61538  29.44444  59.115385  59.961538  31.44828
## Solar.R 181.29630 190.16667 216.483871 171.857143 167.43333
## Wind     11.62258  10.26667   8.941935   8.793548  10.18000

# Splitting on more than one level

x <- rnorm(10)
f1 <- gl(2,5)
f2 <- gl(5,2)
f1

##  [1] 1 1 1 1 1 2 2 2 2 2
## Levels: 1 2

f2

##  [1] 1 1 2 2 3 3 4 4 5 5
## Levels: 1 2 3 4 5

x

##  [1]  1.024069573  0.004974036 -2.339472300  0.124157482  0.102268778
##  [6] -0.189907702 -1.163785840  2.308909538  0.026116701 -0.977754778

y <-data.frame(x,f1,f2)
y

##               x f1 f2
## 1   1.024069573  1  1
## 2   0.004974036  1  1
## 3  -2.339472300  1  2
## 4   0.124157482  1  2
## 5   0.102268778  1  3
## 6  -0.189907702  2  3
## 7  -1.163785840  2  4
## 8   2.308909538  2  4
## 9   0.026116701  2  5
## 10 -0.977754778  2  5

interaction(f1,f2) # interaction computes a factor which represents the interaction of the given factors

##  [1] 1.1 1.1 1.2 1.2 1.3 2.3 2.4 2.4 2.5 2.5
## Levels: 1.1 2.1 1.2 2.2 1.3 2.3 1.4 2.4 1.5 2.5

# interactions can create empty levels

str(split(x,list(f1,f2))) # it will do the interaction function automatically.

## List of 10
##  $ 1.1: num [1:2] 1.02407 0.00497
##  $ 2.1: num(0) 
##  $ 1.2: num [1:2] -2.339 0.124
##  $ 2.2: num(0) 
##  $ 1.3: num 0.102
##  $ 2.3: num -0.19
##  $ 1.4: num(0) 
##  $ 2.4: num [1:2] -1.16 2.31
##  $ 1.5: num(0) 
##  $ 2.5: num [1:2] 0.0261 -0.9778

# Empty levels can be dropped.

str(split(x,list(f1,f2),drop=TRUE))

## List of 6
##  $ 1.1: num [1:2] 1.02407 0.00497
##  $ 1.2: num [1:2] -2.339 0.124
##  $ 1.3: num 0.102
##  $ 2.3: num -0.19
##  $ 2.4: num [1:2] -1.16 2.31
##  $ 2.5: num [1:2] 0.0261 -0.9778

Debugging Tools- Diagnosing the Problem

Debugging tool built in R

indications that something’s not right * message: A generic notification/diagnostic message produced by the message function; execution of the function continues * warning an indicaiton that something is wrong but not necessarily fatal; execution of the function continues; generated by the warning funciton * error: an indication that a fatal problem has occurred; execution stops; produced by the stop funciton * condition: a generic concept for indicating that something uenexpected can occur; programmers can create their own conditions

# log(-1) an error will return

printmessage <- function(x) {
  if(x>0)
    print("x is greater than zero") 
  else
    print("x is less than or equal to zero")
  invisible(x) # the object returned does not get printed in console.
}

printmessage(1)

## [1] "x is greater than zero"

# printmessage(NA) an error will return because you can not make a comparision whethaet NA is greater than zero.

# how to fix it

printmessage2 <- function(x) {
  if(is.na(x))
    print("x is a missing value!")
  else if(x>0)
    print("x is greater than zero")
  else
    print("x is less than or equal to zero")
  invisible(x)
}

printmessage2(NA)

## [1] "x is a missing value!"

How do you know that something is wrong with your function?

• What was your input? How did you call the function?
• What were you expecting? Output, messages, other results?
• What did you get?
• How does what you get differ from what you were expecting?
• Were you expectations correct in the first place?
• Can you reproduce the problem(exactly)

Debugging Tools - Basic Tools

The primary tools for debugging funcitons in R are * traceback: prints out the function call stack after an error occurs; does nothing if there’s no erro * debug: flags a function for “debug” mode which allows you to step through execution of a function one line at a time. * browser: suspends the execution of a funtion whever it is called and puts the function in debug mode * trace: allows you to insert debugging code into a function a specific places * recover: allows you to modifi=y the error behavior so that you can browse the funciton call stack.

These are interactive tools specifically designed to allow you to pick through a funciton. There’s also the more blunt technique of inserting print/cat statements in the function.

Debugging Tools - Using the Tools

# mean(xx) give a warning
# mean(xxx)
# traceback() # traceback give you the most recent error.

Quiz

library(datasets)
data(iris)
?iris

head(iris)

##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa

# In this dataset, what is the mean of 'Sepal.Length' for the species virginica? 
tapply(iris$Sepal.Length,iris$Species,mean)

##     setosa versicolor  virginica 
##      5.006      5.936      6.588

# Continuing with the 'iris' dataset from the previous Question, what R code returns a vector of the means of the variables 'Sepal.Length', 'Sepal.Width', 'Petal.Length', and 'Petal.Width'?

colMeans(iris[,1:4])

## Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
##     5.843333     3.057333     3.758000     1.199333

apply(iris[,1:4],2,mean)

## Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
##     5.843333     3.057333     3.758000     1.199333

library(datasets)
data(mtcars)

?mtcars

head(mtcars)

##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

# How can one calculate the average miles per gallon (mpg) by number of cylinders in the car (cyl)? Select all that apply.


sapply(split(mtcars$mpg, mtcars$cyl), mean)

##        4        6        8 
## 26.66364 19.74286 15.10000

with(mtcars, tapply(mpg, cyl, mean))

##        4        6        8 
## 26.66364 19.74286 15.10000

tapply(mtcars$mpg, mtcars$cyl, mean)

##        4        6        8 
## 26.66364 19.74286 15.10000

# what is the absolute difference between the average horsepower of 4-cylinder cars and the average horsepower of 8-cylinder cars?
x<-tapply(mtcars$hp, mtcars$cyl, mean)
x

##         4         6         8 
##  82.63636 122.28571 209.21429

x[1]-x[3]

##         4 
## -126.5779

debug(ls)
ls()

## debugging in: ls()
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls()

##  [1] "a"             "above"         "above10"       "add2"         
##  [5] "age"           "columnmean"    "count"         "cube"         
##  [9] "data1"         "data2"         "data3"         "data4"        
## [13] "datestring"    "f"             "f1"            "f2"           
## [17] "good"          "i"             "iris"          "j"            
## [21] "letter"        "m"             "make.power"    "msg"          
## [25] "mtcars"        "myplot"        "name"          "noise"        
## [29] "p"             "printmessage"  "printmessage2" "s"            
## [33] "suqre"         "u"             "x"             "y"            
## [37] "z"

Programming Assignment

Example: Caching the Mean of a Vector

The first function, makeVector creates a special “vector”, which is really a list containing a function to

1. set the value of the vector

2. get the value of the vector

3. set the value of the mean

4. get the value of the mean

makeVector <- function(x = numeric()) {
        m <- NULL
        set <- function(y) {
                x <<- y
                m <<- NULL
        }
        get <- function() x # since the symbol x is not defined within get(), R retrieves it from the parent environment
        setmean <- function(mean) m <<- mean # the code uses the <<- form of the assignment operator to assign the input argument to the value of m in the parent environment.
        getmean <- function() m
        list(set = set, get = get,
             setmean = setmean,
             getmean = getmean)
}

makeVector(1:2)

## $set
## function(y) {
##                 x <<- y
##                 m <<- NULL
##         }
## <environment: 0x11adcbc80>
## 
## $get
## function() x
## <environment: 0x11adcbc80>
## 
## $setmean
## function(mean) m <<- mean
## <environment: 0x11adcbc80>
## 
## $getmean
## function() m
## <environment: 0x11adcbc80>

cachemean <- function(x, ...) {
        m <- x$getmean()
        if(!is.null(m)) {
                message("getting cached data")
                return(m)
        }
        data <- x$get()
        m <- mean(data, ...)
        x$setmean(m)
        m
}

aVector <-makeVector(1:10)

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

aVector$get()

##  [1]  1  2  3  4  5  6  7  8  9 10

aVector$getmean()

## NULL

aVector$set(30:50)
cachemean(aVector)

## [1] 40

aVector$getmean()

## [1] 40

Simulation & Profiling

str: compactly display the internal structure of an R object

• A diagnostic function and an alternative to ‘summary’
• It is especially well suited to compactly display the (abbreviated) contents of (possibly nested) lists.
• Roughly one line per basic object

str(str)

## function (object, ...)

str(lm)

## function (formula, data, subset, weights, na.action, method = "qr", model = TRUE, 
##     x = FALSE, y = FALSE, qr = TRUE, singular.ok = TRUE, contrasts = NULL, 
##     offset, ...)

x<-rnorm(100,2,4)
str(x)

##  num [1:100] 5.42 5.23 -1.51 1.72 1.77 ...

summary(x)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -6.6832  0.3383  3.0255  2.8213  5.4315  9.6969

f <- gl(40, 10)
str(f)

##  Factor w/ 40 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...

library(datasets)
head(airquality)

##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 5    NA      NA 14.3   56     5   5
## 6    28      NA 14.9   66     5   6

str(airquality)

## 'data.frame':    153 obs. of  6 variables:
##  $ Ozone  : int  41 36 12 18 NA 28 23 19 8 NA ...
##  $ Solar.R: int  190 118 149 313 NA NA 299 99 19 194 ...
##  $ Wind   : num  7.4 8 12.6 11.5 14.3 14.9 8.6 13.8 20.1 8.6 ...
##  $ Temp   : int  67 72 74 62 56 66 65 59 61 69 ...
##  $ Month  : int  5 5 5 5 5 5 5 5 5 5 ...
##  $ Day    : int  1 2 3 4 5 6 7 8 9 10 ...

m <- matrix(rnorm(100), 10, 10)
str(m) # give you the observation in first column

##  num [1:10, 1:10] 0.343 -2.262 -0.372 0.889 0.119 ...

s<-split(airquality, airquality$Month)
str(s)

## List of 5
##  $ 5:'data.frame':   31 obs. of  6 variables:
##   ..$ Ozone  : int [1:31] 41 36 12 18 NA 28 23 19 8 NA ...
##   ..$ Solar.R: int [1:31] 190 118 149 313 NA NA 299 99 19 194 ...
##   ..$ Wind   : num [1:31] 7.4 8 12.6 11.5 14.3 14.9 8.6 13.8 20.1 8.6 ...
##   ..$ Temp   : int [1:31] 67 72 74 62 56 66 65 59 61 69 ...
##   ..$ Month  : int [1:31] 5 5 5 5 5 5 5 5 5 5 ...
##   ..$ Day    : int [1:31] 1 2 3 4 5 6 7 8 9 10 ...
##  $ 6:'data.frame':   30 obs. of  6 variables:
##   ..$ Ozone  : int [1:30] NA NA NA NA NA NA 29 NA 71 39 ...
##   ..$ Solar.R: int [1:30] 286 287 242 186 220 264 127 273 291 323 ...
##   ..$ Wind   : num [1:30] 8.6 9.7 16.1 9.2 8.6 14.3 9.7 6.9 13.8 11.5 ...
##   ..$ Temp   : int [1:30] 78 74 67 84 85 79 82 87 90 87 ...
##   ..$ Month  : int [1:30] 6 6 6 6 6 6 6 6 6 6 ...
##   ..$ Day    : int [1:30] 1 2 3 4 5 6 7 8 9 10 ...
##  $ 7:'data.frame':   31 obs. of  6 variables:
##   ..$ Ozone  : int [1:31] 135 49 32 NA 64 40 77 97 97 85 ...
##   ..$ Solar.R: int [1:31] 269 248 236 101 175 314 276 267 272 175 ...
##   ..$ Wind   : num [1:31] 4.1 9.2 9.2 10.9 4.6 10.9 5.1 6.3 5.7 7.4 ...
##   ..$ Temp   : int [1:31] 84 85 81 84 83 83 88 92 92 89 ...
##   ..$ Month  : int [1:31] 7 7 7 7 7 7 7 7 7 7 ...
##   ..$ Day    : int [1:31] 1 2 3 4 5 6 7 8 9 10 ...
##  $ 8:'data.frame':   31 obs. of  6 variables:
##   ..$ Ozone  : int [1:31] 39 9 16 78 35 66 122 89 110 NA ...
##   ..$ Solar.R: int [1:31] 83 24 77 NA NA NA 255 229 207 222 ...
##   ..$ Wind   : num [1:31] 6.9 13.8 7.4 6.9 7.4 4.6 4 10.3 8 8.6 ...
##   ..$ Temp   : int [1:31] 81 81 82 86 85 87 89 90 90 92 ...
##   ..$ Month  : int [1:31] 8 8 8 8 8 8 8 8 8 8 ...
##   ..$ Day    : int [1:31] 1 2 3 4 5 6 7 8 9 10 ...
##  $ 9:'data.frame':   30 obs. of  6 variables:
##   ..$ Ozone  : int [1:30] 96 78 73 91 47 32 20 23 21 24 ...
##   ..$ Solar.R: int [1:30] 167 197 183 189 95 92 252 220 230 259 ...
##   ..$ Wind   : num [1:30] 6.9 5.1 2.8 4.6 7.4 15.5 10.9 10.3 10.9 9.7 ...
##   ..$ Temp   : int [1:30] 91 92 93 93 87 84 80 78 75 73 ...
##   ..$ Month  : int [1:30] 9 9 9 9 9 9 9 9 9 9 ...
##   ..$ Day    : int [1:30] 1 2 3 4 5 6 7 8 9 10 ...

Simulation - generating random numbers

Functions for probability distributions in R * rnorm: generate random Normal variates with a given mean and standard deviation. * dnorm: evaluate the Normal probability density (with a given mean/SD) at a point (or vector of points). * pnorm : evaluate the cumulative distribution funciton for a Normal distribution. * rpois : generate random Poisson vaariates with a given rate.

Probability distribution functions usually have four functions associated with them. The functions are preficed with a * d for density * r for random number generation * p for cumulative distribution * q for quantile function

working with the normal distributions requires using these four functions

# dnorm(x, mean=0, sd=1, log=F)
# pnorm(q, mean=0, sd=1, lower.tail =T, log.p=F)
# qnorm(q, mean=0, sd=1, lower.tail =T, log.p=F)
# rnorm(n, mean=0,sd=1)

x <-rnorm(10)
x

##  [1] -0.7530543  0.3407483 -1.0839355 -0.4138759 -1.8711146  0.7096290
##  [7]  0.1446385 -1.8526195 -0.4921620  1.9224461

x <- rnorm(10,20,2)

set.seed(1)
rnorm(5)

## [1] -0.6264538  0.1836433 -0.8356286  1.5952808  0.3295078

set.seed(1)
rnorm(5)

## [1] -0.6264538  0.1836433 -0.8356286  1.5952808  0.3295078

# generat Poisson data

rpois(10,1)

##  [1] 0 0 1 1 2 1 1 4 1 2

rpois(10,2)

##  [1] 4 1 2 0 1 1 0 1 4 1

ppois(4,2) # cummulative distribution Pr(x <=4)

## [1] 0.947347

Simulation - simulating a linear model

set.seed(20)
x <- rnorm(100)
e <- rnorm(100, 0, 2)

y <- 0.5+ 2*x + e

summary(y)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -6.4084 -1.5402  0.6789  0.6893  2.9303  6.5052

plot(x,y)

what if x is binary

set.seed(10)
x <- rbinom(100, 1, 0.5)
y <- 0.5+ 2*x + e

summary(y)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -3.07774  0.03846  1.24754  1.51949  3.21966  6.01715

plot(x,y)

Suppose we want to simulate from a Poisson model

set.seed(1)
x <- rnorm(100)
log.mu <- 0.5+0.3*x
y <- rpois(100, exp(log.mu))

summary(y)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00    1.00    1.00    1.55    2.00    6.00

plot(x,y)

### Simulation - Random Sampling

# The sample function draws randomly from a specified set of (scalar) objects allowing you to sample from arbitrary distributions.

set.seed(1)

sample(1:10,4)

## [1] 9 4 7 1

sample(letters,5)

## [1] "b" "w" "k" "n" "r"

sample(1:10) # permutation

##  [1]  3  1  5  8  2  6 10  9  4  7

sample(1:10,replace=T) # sample with replacement

##  [1]  5  9  9  5  5  2 10  9  1  4

R profiler

Why is my code so slow? * profiling is a systematic way to examine how much time is spend in different parts of a program * Useful when trying to optimize your code * Often code runs fine once, but what if you have to put it in a loop for 1000 iterations? Is it still fast enough? * Profiling is better than guessing.

On optimizing your code * Getting biggest impact on speeding up code depends on knowing where the code spends most of its time * This cannot be done withou performance analysis or profiling

Using system.time() * user time: time charged to the cpu for this expression * elapsed itme:” wall clock” time

system.time(readLines("http://www.jhsph.edu"))

##    user  system elapsed 
##   0.042   0.006   0.631

The Rprof() function strarts the profiler in R * R must be compiled with profiler support ( but this is usually the case) The summaryRprof() function summarizes the output from Rprof() (otherwise its not readable) * Do not use system.teim() and Rprof() togehter or you will be sad.

Course 8 Practical Machine Learning

week 8.1 Prediciton

Who predicts

• Local governments - > pension payments
• Google -> Whether you will click on an ad
• Amazon -> what movies you will watch
• Insurance companies -> what your risk of death is
• Johns Hopkins -> who will succeed in their programs

Componets of a predictor

*question -> input data -> features -> algorithm -> parameters -> evaluation

example: start with a general question can I automatically detect emails that are SPAM that are not make it concrete Can i use quantitative characteristics of the emails to classify them as SPAM / HAM?

Relative order of importance:

question > data > features > algorithms

colleting the right data and the data is relvant to the question you are trying to answer. Often more data > better models

Properties of good features * lead to data compression * retain relevant information * are created based on expert application knowledge

Common mistakes * trying to automate feature selection * not paying attention to data-specific quirks * throwing away information unnecessarily

Algorithms matter less than you’d think

The “Best” machine Learning method * interpretable, simple, accurate, fast ( to train and test), scalable ( easy to apply to a large dataset.)

Prediciton is about accuracy tradeoffs

• interpretability versus accuracy
• speed versus accuracy
• simplicity versus accuracy
• scalability versus accuracy

In sample and out of smaple error

In sample error: the error rate you get on the same data set you used to build your predictor. Sometimes called resubsititution error.

Out of smaple error: the error rate you get on a new data set. sometimes called generalization error.

Key ides 1. out of smaple error is what you care about 2. in sample error < out of smaple error 3. the reason is overfitting * matching your algorithm to the data you have.

Why more sophscated alogrithm yield higher out of sample error” * overfitting + data have two parts: signal and noise * the goal of a predictor is to find signal * you can always design a perfect in-sample predictor * you capture both signal + noise when you do that * predictor won’t perform as well on new samples

Prdiction study design

1. Define your error rate
2. Split data into :

• training, testing, validation (optional)

3. On thetraining set pick features

• use cross-validation

4. ON the training set pick prediction function

• use cross-validation

5. If no validation

• apply 1 time to test set

6. if validation

• apply to test set and refine
• apply 1* to validation

Avioid small sample sizes.

• if you have a lrge sample size

• 60% training

• 20% test

• 20% validation

• if you have a medium sample size -60% training -40 % testing

*if you have a small sample size - do cross validation - report caveat of small sample size

some principles to remember

set the test/validaiton set aside and don’t look at it all subsets should reflect as much diversity as possible -you can also try to balance by features - but this is tricky

types of error

sensitivity = tp/(tp+FN) 真得病的有多少可以测出来 recall

specificity = tn/(FP+TN) 真没病的有多少可以测出来

positive predictive value = TP/TP+FP 测出有病的有多少是真有病 precision negative predictive value = TN/FN+TN 测出没病的有多少是真没病

accuracy = (TP+TN)/(TP+FP+FN+TN) 测得有多准

For continuous data: mean squared error(MSE): calculate the average of the suqared differences between prediction and truth.

Root mean squared error (RMSE) square root of the previous A good measure of the error of the continuos data.

common error measures

1. mean squared error ( continuous data, sensitive to outliers
2. median absolute deviation (continuous data. often more robust)
3. sensity (recall)
4. specificity
5. accuracy

Receiver Operating Charactristic

ROC curves

a common way to measure the quality or goodness of a prediction algorithm.

Why a curve? * in binary classification you are predicting one of two categories

• but your predictions are ofoten quantitative -probability of being alive

• the cutoff you choose gives different results

senstivity( recall) on the y axis (true positive rate) (1-specificity) on the x axis (false positive rate)

different point represnt different cutoff

this curve shows the tradeoff between specificity and senstivity

AUC area under the cure to compare the performace of different algothrim

if AUC =0 .5: random guessing if AUX =1 ” perfect classifer in general AUC of above 0.8 considered good

cross validation

This lecture is about cross validation. Which is one of the most widely used tools, for detecting relevant features, and for building models. And estimating their parameters when doing machine learning.

Approach: 1. use the training set 2. split it into training/test sets 3. build a odel on the training set 4. evaluate on the test set 5. repeat and average the estimated errors

used for: 1. picking variables to include in a model 2. picking the tpe of prediction function to use 3. picking the parameters in the prediction function 4. compare different predictors

So, the different ways that people can use training and test sets. One example is they do random subsampling. So, imagine that, every observation we’re trying to predict is arrayed out along the, this axis here. And the color represents whether we include it in the training set or testing set, so again, this is only the training samples, and what we might do is just take a subsample of them, and call them the testing sample. So in this case, it’s the light gray bars here, are all the samples in this particular iteration that we call test samples. Then we would build our predictor on all the dark gray samples. And so, again, this is only within the training set. We take the dark gray samples and build a model, and then apply it to predict the light gray samples, and evaluate their accuracy. We can do this, for several different random subsamples. So this is a ra, one random sampling. And then this second row is the second random sampling. And this third row is the third random sampling. Do that over and over again, and then average what the errors will be.

Another way is called K-fold cross validation

another way is called leave one out cross validation

Considerations * for time series data, data must be used in “chunks” * for k-fold cross validation + larger k= less bias, more variance + smaller k = more bias, less variamce * random sampling must be done without replacement * random sampling with replacement is the bootstrap + underestimates of the erorr + can be corrected, but it is complicated

• if you cross-validate to pick predictors estimate you must estimate errors on independent data.

Week 8.2 Caret package

Caret functionality

• some preprocessing (cleanihng)
  • preProcess
• Data spliting
  • createDataPartition
  • createResample
  • createTimeSlices
• Training/testing functions
  • train
  • predict
• Model comparison
  • confusionMatrix

Machine Learning algorithms in R

• Linear discriminant analysis
• Regression
• Naive Bayes
• Support vector machines
• Classification and regression trees
• Random forests
• Boosting
• etc.

SPAM Example: Data splitting

library(caret)

## Loading required package: ggplot2

## Loading required package: lattice

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

# install.packages("kernlab")
library(kernlab);data(spam) # load the spam dataset

## 
## Attaching package: 'kernlab'

## The following object is masked from 'package:ggplot2':
## 
##     alpha

inTrain <- createDataPartition(y=spam$type,p=0.75, list=FALSE) # split the data set in to 75% training

training <- spam[inTrain,]
testing <- spam[-inTrain,]

dim(training)

## [1] 3451   58

SPAM Example: Fit a model

set.seed(32343)
modelFit <- train(type~., data=training, method="glm")

## debugging in: ls(env, pattern = p, all.names = TRUE)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##     length(grep("]", pattern, fixed = TRUE))) {
##     if (pattern == "[") {
##         pattern <- "\\["
##         warning("replaced regular expression pattern '[' by  '\\\\['")
##     }
##     else if (length(grep("[^\\\\]\\[<-", pattern))) {
##         pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##         warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##     }
## }
## debug: grep(pattern, all.names, value = TRUE)
## exiting from: ls(env, pattern = p, all.names = TRUE)
## debugging in: ls(env, pattern = p, all.names = TRUE)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##     length(grep("]", pattern, fixed = TRUE))) {
##     if (pattern == "[") {
##         pattern <- "\\["
##         warning("replaced regular expression pattern '[' by  '\\\\['")
##     }
##     else if (length(grep("[^\\\\]\\[<-", pattern))) {
##         pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##         warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##     }
## }
## debug: grep(pattern, all.names, value = TRUE)
## exiting from: ls(env, pattern = p, all.names = TRUE)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: algorithm did not converge

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

modelFit

## Generalized Linear Model 
## 
## 3451 samples
##   57 predictor
##    2 classes: 'nonspam', 'spam' 
## 
## No pre-processing
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 3451, 3451, 3451, 3451, 3451, 3451, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.9225736  0.8371828

modelFit$finalModel # get the details of the fitted model parameter.

## 
## Call:  NULL
## 
## Coefficients:
##       (Intercept)               make            address                all  
##        -1.620e+00         -5.885e-01         -1.190e-01          1.661e-01  
##             num3d                our               over             remove  
##         2.636e+00          5.691e-01          7.279e-01          2.458e+00  
##          internet              order               mail            receive  
##         6.518e-01          1.059e+00          9.496e-02         -7.488e-02  
##              will             people             report          addresses  
##        -8.175e-02         -4.441e-02          6.955e-02          1.712e+00  
##              free           business              email                you  
##         9.414e-01          1.443e+00          9.566e-02          6.401e-02  
##            credit               your               font             num000  
##         1.407e+00          2.144e-01          2.940e-01          1.837e+00  
##             money                 hp                hpl             george  
##         6.259e-01         -2.089e+00         -8.787e-01         -1.129e+01  
##            num650                lab               labs             telnet  
##         4.358e-01         -4.073e+00         -2.792e-01         -1.282e-01  
##            num857               data             num415              num85  
##         2.261e+00         -7.452e-01          5.336e-01         -1.852e+00  
##        technology            num1999              parts                 pm  
##         1.245e+00         -2.546e-02          9.555e-01         -1.011e+00  
##            direct                 cs            meeting           original  
##        -2.261e-01         -5.235e+02         -2.362e+00         -1.907e+00  
##           project                 re                edu              table  
##        -1.599e+00         -5.858e-01         -1.619e+00         -2.120e+00  
##        conference      charSemicolon   charRoundbracket  charSquarebracket  
##        -3.425e+00         -1.508e+00         -4.612e-01         -8.961e-01  
##   charExclamation         charDollar           charHash         capitalAve  
##         6.385e-01          5.002e+00          2.195e+00          6.768e-03  
##       capitalLong       capitalTotal  
##         9.550e-03          6.548e-04  
## 
## Degrees of Freedom: 3450 Total (i.e. Null);  3393 Residual
## Null Deviance:       4628 
## Residual Deviance: 1336  AIC: 1452

predictions <- predict(modelFit, newdata=testing)
predictions

##    [1] spam    spam    spam    spam    spam    spam    spam    spam    nonspam
##   [10] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##   [19] spam    spam    spam    spam    spam    spam    spam    nonspam spam   
##   [28] nonspam spam    spam    spam    spam    spam    spam    spam    spam   
##   [37] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##   [46] spam    spam    spam    nonspam spam    spam    spam    spam    spam   
##   [55] spam    spam    spam    spam    spam    nonspam spam    spam    spam   
##   [64] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##   [73] spam    spam    spam    spam    spam    spam    nonspam spam    spam   
##   [82] nonspam spam    spam    spam    spam    spam    spam    spam    spam   
##   [91] spam    spam    spam    spam    spam    spam    spam    nonspam spam   
##  [100] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [109] spam    spam    spam    nonspam spam    spam    spam    spam    spam   
##  [118] nonspam spam    nonspam nonspam spam    nonspam spam    spam    spam   
##  [127] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [136] spam    spam    spam    spam    nonspam spam    spam    spam    spam   
##  [145] nonspam spam    spam    spam    spam    spam    nonspam spam    spam   
##  [154] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [163] spam    spam    nonspam spam    spam    spam    spam    spam    spam   
##  [172] spam    nonspam spam    spam    spam    spam    spam    spam    spam   
##  [181] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [190] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [199] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [208] spam    spam    spam    spam    spam    spam    spam    nonspam spam   
##  [217] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [226] spam    spam    spam    nonspam spam    nonspam nonspam spam    spam   
##  [235] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [244] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [253] spam    spam    nonspam spam    spam    spam    spam    spam    spam   
##  [262] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [271] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [280] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [289] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [298] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [307] spam    nonspam spam    spam    spam    spam    spam    spam    spam   
##  [316] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [325] spam    nonspam spam    spam    spam    spam    spam    spam    spam   
##  [334] nonspam nonspam nonspam spam    spam    spam    nonspam spam    spam   
##  [343] spam    spam    spam    spam    spam    spam    spam    spam    spam   
##  [352] nonspam spam    spam    nonspam nonspam spam    spam    spam    spam   
##  [361] spam    spam    spam    nonspam spam    spam    spam    spam    spam   
##  [370] spam    spam    spam    spam    nonspam spam    spam    spam    spam   
##  [379] spam    spam    spam    spam    spam    spam    spam    spam    nonspam
##  [388] spam    nonspam spam    nonspam spam    spam    spam    spam    spam   
##  [397] nonspam nonspam spam    spam    spam    spam    spam    spam    spam   
##  [406] spam    spam    spam    spam    nonspam spam    spam    spam    spam   
##  [415] nonspam spam    spam    spam    nonspam nonspam spam    spam    spam   
##  [424] spam    spam    spam    nonspam spam    spam    nonspam spam    spam   
##  [433] spam    spam    spam    spam    spam    spam    nonspam spam    spam   
##  [442] spam    spam    spam    spam    nonspam spam    spam    spam    spam   
##  [451] nonspam spam    spam    spam    nonspam nonspam nonspam nonspam nonspam
##  [460] nonspam nonspam spam    nonspam nonspam nonspam nonspam nonspam nonspam
##  [469] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [478] nonspam nonspam spam    nonspam nonspam nonspam nonspam nonspam nonspam
##  [487] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [496] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [505] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [514] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [523] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [532] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [541] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [550] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [559] nonspam spam    nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [568] nonspam nonspam nonspam nonspam nonspam nonspam nonspam spam    nonspam
##  [577] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [586] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [595] nonspam spam    nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [604] nonspam nonspam nonspam nonspam nonspam nonspam spam    nonspam nonspam
##  [613] nonspam nonspam nonspam nonspam nonspam nonspam spam    nonspam nonspam
##  [622] nonspam nonspam nonspam nonspam nonspam nonspam spam    nonspam nonspam
##  [631] nonspam nonspam nonspam nonspam nonspam spam    nonspam nonspam nonspam
##  [640] spam    nonspam nonspam nonspam spam    nonspam nonspam nonspam nonspam
##  [649] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [658] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam spam   
##  [667] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [676] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [685] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [694] nonspam nonspam nonspam nonspam nonspam nonspam nonspam spam    nonspam
##  [703] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [712] nonspam nonspam nonspam nonspam nonspam spam    nonspam nonspam nonspam
##  [721] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [730] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [739] nonspam spam    nonspam nonspam nonspam nonspam nonspam nonspam spam   
##  [748] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [757] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [766] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [775] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [784] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [793] nonspam nonspam nonspam nonspam nonspam nonspam nonspam spam    nonspam
##  [802] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [811] nonspam nonspam spam    nonspam nonspam nonspam nonspam nonspam nonspam
##  [820] nonspam nonspam nonspam nonspam nonspam nonspam spam    nonspam nonspam
##  [829] spam    nonspam nonspam spam    spam    nonspam nonspam nonspam nonspam
##  [838] nonspam nonspam nonspam nonspam spam    nonspam nonspam nonspam nonspam
##  [847] nonspam nonspam nonspam nonspam spam    nonspam nonspam nonspam nonspam
##  [856] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [865] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [874] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [883] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [892] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [901] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [910] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [919] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [928] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [937] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [946] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [955] nonspam nonspam nonspam spam    nonspam nonspam nonspam nonspam nonspam
##  [964] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [973] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [982] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
##  [991] nonspam nonspam nonspam nonspam nonspam spam    nonspam nonspam nonspam
## [1000] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1009] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1018] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1027] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1036] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1045] nonspam spam    nonspam nonspam nonspam nonspam nonspam nonspam spam   
## [1054] spam    nonspam nonspam spam    nonspam nonspam nonspam nonspam nonspam
## [1063] spam    nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1072] nonspam nonspam nonspam spam    nonspam nonspam nonspam nonspam nonspam
## [1081] nonspam nonspam nonspam spam    nonspam nonspam nonspam nonspam nonspam
## [1090] nonspam spam    nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1099] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1108] nonspam nonspam nonspam nonspam spam    nonspam nonspam nonspam nonspam
## [1117] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1126] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1135] nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## [1144] nonspam nonspam nonspam nonspam nonspam nonspam nonspam
## Levels: nonspam spam

SPAM Example: Confusion Matrix

check the model preformance

# confusionMatrix(predicitons, testing$type)

Data slicing

SPAM Example: Data splitting

Use createDataPartition to separate training set and test set.

library(caret)
library(kernlab);data(spam) # load the spam dataset

# create an indicator function.
inTrain <- createDataPartition(y=spam$type,p=0.75, list=FALSE) # split the data set in to 75% training

training <- spam[inTrain,]
testing <- spam[-inTrain,]

dim(training)

## [1] 3451   58

SPAM Example: K-fold of the training set

set.seed(32323)
folds <- createFolds(y=spam$type, k=10, list=T, returnTrain=T)

sapply(folds, length)

## Fold01 Fold02 Fold03 Fold04 Fold05 Fold06 Fold07 Fold08 Fold09 Fold10 
##   4140   4142   4141   4140   4141   4141   4142   4141   4141   4140

folds[[1]][1:10]

##  [1]  1  2  4  5  6  7  8  9 10 11

table(unlist(folds)) # each observation to be used in 9 of the folds.

## 
##    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##   17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##   33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##   49   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##   65   66   67   68   69   70   71   72   73   74   75   76   77   78   79   80 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##   81   82   83   84   85   86   87   88   89   90   91   92   93   94   95   96 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##   97   98   99  100  101  102  103  104  105  106  107  108  109  110  111  112 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##  113  114  115  116  117  118  119  120  121  122  123  124  125  126  127  128 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##  129  130  131  132  133  134  135  136  137  138  139  140  141  142  143  144 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##  145  146  147  148  149  150  151  152  153  154  155  156  157  158  159  160 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##  161  162  163  164  165  166  167  168  169  170  171  172  173  174  175  176 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
##  177  178  179  180  181  182  183  184  185  186  187  188  189  190  191  192 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
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##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
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##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 3921 3922 3923 3924 3925 3926 3927 3928 3929 3930 3931 3932 3933 3934 3935 3936 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 3937 3938 3939 3940 3941 3942 3943 3944 3945 3946 3947 3948 3949 3950 3951 3952 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 3953 3954 3955 3956 3957 3958 3959 3960 3961 3962 3963 3964 3965 3966 3967 3968 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 3969 3970 3971 3972 3973 3974 3975 3976 3977 3978 3979 3980 3981 3982 3983 3984 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 3985 3986 3987 3988 3989 3990 3991 3992 3993 3994 3995 3996 3997 3998 3999 4000 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4001 4002 4003 4004 4005 4006 4007 4008 4009 4010 4011 4012 4013 4014 4015 4016 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4017 4018 4019 4020 4021 4022 4023 4024 4025 4026 4027 4028 4029 4030 4031 4032 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044 4045 4046 4047 4048 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4049 4050 4051 4052 4053 4054 4055 4056 4057 4058 4059 4060 4061 4062 4063 4064 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4065 4066 4067 4068 4069 4070 4071 4072 4073 4074 4075 4076 4077 4078 4079 4080 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4081 4082 4083 4084 4085 4086 4087 4088 4089 4090 4091 4092 4093 4094 4095 4096 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4097 4098 4099 4100 4101 4102 4103 4104 4105 4106 4107 4108 4109 4110 4111 4112 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4113 4114 4115 4116 4117 4118 4119 4120 4121 4122 4123 4124 4125 4126 4127 4128 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4129 4130 4131 4132 4133 4134 4135 4136 4137 4138 4139 4140 4141 4142 4143 4144 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4145 4146 4147 4148 4149 4150 4151 4152 4153 4154 4155 4156 4157 4158 4159 4160 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4161 4162 4163 4164 4165 4166 4167 4168 4169 4170 4171 4172 4173 4174 4175 4176 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4177 4178 4179 4180 4181 4182 4183 4184 4185 4186 4187 4188 4189 4190 4191 4192 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4193 4194 4195 4196 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4209 4210 4211 4212 4213 4214 4215 4216 4217 4218 4219 4220 4221 4222 4223 4224 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4225 4226 4227 4228 4229 4230 4231 4232 4233 4234 4235 4236 4237 4238 4239 4240 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4241 4242 4243 4244 4245 4246 4247 4248 4249 4250 4251 4252 4253 4254 4255 4256 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4257 4258 4259 4260 4261 4262 4263 4264 4265 4266 4267 4268 4269 4270 4271 4272 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4273 4274 4275 4276 4277 4278 4279 4280 4281 4282 4283 4284 4285 4286 4287 4288 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4289 4290 4291 4292 4293 4294 4295 4296 4297 4298 4299 4300 4301 4302 4303 4304 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4305 4306 4307 4308 4309 4310 4311 4312 4313 4314 4315 4316 4317 4318 4319 4320 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4321 4322 4323 4324 4325 4326 4327 4328 4329 4330 4331 4332 4333 4334 4335 4336 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4337 4338 4339 4340 4341 4342 4343 4344 4345 4346 4347 4348 4349 4350 4351 4352 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4353 4354 4355 4356 4357 4358 4359 4360 4361 4362 4363 4364 4365 4366 4367 4368 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4369 4370 4371 4372 4373 4374 4375 4376 4377 4378 4379 4380 4381 4382 4383 4384 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4385 4386 4387 4388 4389 4390 4391 4392 4393 4394 4395 4396 4397 4398 4399 4400 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4401 4402 4403 4404 4405 4406 4407 4408 4409 4410 4411 4412 4413 4414 4415 4416 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4417 4418 4419 4420 4421 4422 4423 4424 4425 4426 4427 4428 4429 4430 4431 4432 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4433 4434 4435 4436 4437 4438 4439 4440 4441 4442 4443 4444 4445 4446 4447 4448 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4449 4450 4451 4452 4453 4454 4455 4456 4457 4458 4459 4460 4461 4462 4463 4464 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4465 4466 4467 4468 4469 4470 4471 4472 4473 4474 4475 4476 4477 4478 4479 4480 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4481 4482 4483 4484 4485 4486 4487 4488 4489 4490 4491 4492 4493 4494 4495 4496 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4497 4498 4499 4500 4501 4502 4503 4504 4505 4506 4507 4508 4509 4510 4511 4512 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4513 4514 4515 4516 4517 4518 4519 4520 4521 4522 4523 4524 4525 4526 4527 4528 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4529 4530 4531 4532 4533 4534 4535 4536 4537 4538 4539 4540 4541 4542 4543 4544 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4545 4546 4547 4548 4549 4550 4551 4552 4553 4554 4555 4556 4557 4558 4559 4560 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4561 4562 4563 4564 4565 4566 4567 4568 4569 4570 4571 4572 4573 4574 4575 4576 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4577 4578 4579 4580 4581 4582 4583 4584 4585 4586 4587 4588 4589 4590 4591 4592 
##    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9    9 
## 4593 4594 4595 4596 4597 4598 4599 4600 4601 
##    9    9    9    9    9    9    9    9    9

# returntraina: logical. When true, the values returned are the sample positions corresponding to the data used during training. This argument only works in conjunction with list = TRUE

SPAM Example: Return test

set.seed(32323)
folds <- createFolds(y=spam$type, k=10, list=T, returnTrain=F)
sapply(folds, length)

## Fold01 Fold02 Fold03 Fold04 Fold05 Fold06 Fold07 Fold08 Fold09 Fold10 
##    461    459    460    461    460    460    459    460    460    461

folds[[1]][1:10]

##  [1]  3 19 33 38 44 51 66 67 72 83

# if return Train is fals, then it would be ten folds for the test set.

SPAM Example: Resampling

set.seed(32323)
folds <- createResample(y=spam$type, times=10,list=T)
sapply(folds, length)

## Resample01 Resample02 Resample03 Resample04 Resample05 Resample06 Resample07 
##       4601       4601       4601       4601       4601       4601       4601 
## Resample08 Resample09 Resample10 
##       4601       4601       4601

folds[[1]][1:10]

##  [1] 1 1 2 2 3 3 4 5 5 7

# sampling with replacement.

SPAM Example: Time slices

set.seed(32323)
tme <- 1:1000
folds <- createTimeSlices(y=tme, initialWindow = 20 , horizon=10)
names(folds)

## [1] "train" "test"

folds$train[[1]]

##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20

folds$test[[1]]

##  [1] 21 22 23 24 25 26 27 28 29 30

Training options

library(caret)
library(kernlab);data(spam) # load the spam dataset

# create an indicator function.
inTrain <- createDataPartition(y=spam$type,p=0.75, list=FALSE) # split the data set in to 75% training

training <- spam[inTrain,]
testing <- spam[-inTrain,]

dim(training)

## [1] 3451   58

modelFit <- train(type~., data=training, method="glm")

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

modelFit

## Generalized Linear Model 
## 
## 3451 samples
##   57 predictor
##    2 classes: 'nonspam', 'spam' 
## 
## No pre-processing
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 3451, 3451, 3451, 3451, 3451, 3451, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.9241196  0.8395629

Ploting predictors

# install.packages("ISLR")
library(ISLR)

## debugging in: ls(env, pattern = p, all.names = TRUE)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##     length(grep("]", pattern, fixed = TRUE))) {
##     if (pattern == "[") {
##         pattern <- "\\["
##         warning("replaced regular expression pattern '[' by  '\\\\['")
##     }
##     else if (length(grep("[^\\\\]\\[<-", pattern))) {
##         pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##         warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##     }
## }
## debug: grep(pattern, all.names, value = TRUE)
## exiting from: ls(env, pattern = p, all.names = TRUE)

library(ggplot2)
library(caret)
data(Wage)
summary(Wage)

##       year           age                     maritl           race     
##  Min.   :2003   Min.   :18.00   1. Never Married: 648   1. White:2480  
##  1st Qu.:2004   1st Qu.:33.75   2. Married      :2074   2. Black: 293  
##  Median :2006   Median :42.00   3. Widowed      :  19   3. Asian: 190  
##  Mean   :2006   Mean   :42.41   4. Divorced     : 204   4. Other:  37  
##  3rd Qu.:2008   3rd Qu.:51.00   5. Separated    :  55                  
##  Max.   :2009   Max.   :80.00                                          
##                                                                        
##               education                     region               jobclass   
##  1. < HS Grad      :268   2. Middle Atlantic   :3000   1. Industrial :1544  
##  2. HS Grad        :971   1. New England       :   0   2. Information:1456  
##  3. Some College   :650   3. East North Central:   0                        
##  4. College Grad   :685   4. West North Central:   0                        
##  5. Advanced Degree:426   5. South Atlantic    :   0                        
##                           6. East South Central:   0                        
##                           (Other)              :   0                        
##             health      health_ins      logwage           wage       
##  1. <=Good     : 858   1. Yes:2083   Min.   :3.000   Min.   : 20.09  
##  2. >=Very Good:2142   2. No : 917   1st Qu.:4.447   1st Qu.: 85.38  
##                                      Median :4.653   Median :104.92  
##                                      Mean   :4.654   Mean   :111.70  
##                                      3rd Qu.:4.857   3rd Qu.:128.68  
##                                      Max.   :5.763   Max.   :318.34  
## 

# get training/test sets
inTrain <- createDataPartition(y=Wage$wage, p=0.7, list=F)

training <- Wage[inTrain,]
testing <- Wage[-inTrain,]

dim(training);

## [1] 2102   11

dim(testing)

## [1] 898  11

# feature plot( caret package )
featurePlot(x=training[,c("age","education","jobclass")],
  y=training$wage,
  plot="pairs")

# Qplot (ggplot2 package)
qplot(age,wage,data=training)

# Qplot with color (ggplot2 package)
qplot(age,wage,colour=jobclass, data=training)

# add regression smoothers (ggplot2 package)
qq <- qplot(age, wage, colour=education, data=training)
qq + geom_smooth(method='lm', formula=y~x)

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

# cut2, makin factors (Hmisc package)
# install.packages("Hmisc")
# change wage variable into different category
library(Hmisc)

## Loading required package: survival

## 
## Attaching package: 'survival'

## The following object is masked from 'package:caret':
## 
##     cluster

## Loading required package: Formula

## debugging in: ls(env, pattern = p, all.names = TRUE)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##     length(grep("]", pattern, fixed = TRUE))) {
##     if (pattern == "[") {
##         pattern <- "\\["
##         warning("replaced regular expression pattern '[' by  '\\\\['")
##     }
##     else if (length(grep("[^\\\\]\\[<-", pattern))) {
##         pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##         warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##     }
## }
## debug: grep(pattern, all.names, value = TRUE)
## exiting from: ls(env, pattern = p, all.names = TRUE)
## debugging in: ls(env, pattern = p, all.names = TRUE)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##     length(grep("]", pattern, fixed = TRUE))) {
##     if (pattern == "[") {
##         pattern <- "\\["
##         warning("replaced regular expression pattern '[' by  '\\\\['")
##     }
##     else if (length(grep("[^\\\\]\\[<-", pattern))) {
##         pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##         warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##     }
## }
## debug: grep(pattern, all.names, value = TRUE)
## exiting from: ls(env, pattern = p, all.names = TRUE)
## debugging in: ls(env, pattern = p, all.names = TRUE)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##     length(grep("]", pattern, fixed = TRUE))) {
##     if (pattern == "[") {
##         pattern <- "\\["
##         warning("replaced regular expression pattern '[' by  '\\\\['")
##     }
##     else if (length(grep("[^\\\\]\\[<-", pattern))) {
##         pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##         warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##     }
## }
## debug: grep(pattern, all.names, value = TRUE)
## exiting from: ls(env, pattern = p, all.names = TRUE)

## 
## Attaching package: 'Hmisc'

## The following objects are masked from 'package:dplyr':
## 
##     src, summarize

## The following objects are masked from 'package:base':
## 
##     format.pval, units

cutWage <- cut2(training$wage, g=3)
table(cutWage)

## cutWage
## [ 20.1, 91.7) [ 91.7,118.9) [118.9,318.3] 
##           701           728           673

p1 <- qplot(cutWage, age, data=training, fill=cutWage, geom=c("boxplot"))

p1

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

# Boxplots with points overlayed
p2 <- qplot(cutWage, age, data=training, fill=cutWage,geom=c("boxplot","jitter"))

# put two picures together.
# grid.arrange(p1,p2,ncol=2)


# Tables

t1 <- table(cutWage,training$jobclass)
t1

##                
## cutWage         1. Industrial 2. Information
##   [ 20.1, 91.7)           442            259
##   [ 91.7,118.9)           370            358
##   [118.9,318.3]           254            419

prop.table(t1,1) # proportion

##                
## cutWage         1. Industrial 2. Information
##   [ 20.1, 91.7)     0.6305278      0.3694722
##   [ 91.7,118.9)     0.5082418      0.4917582
##   [118.9,318.3]     0.3774146      0.6225854

# Density plots

qplot(wage, colour=education, data=training, geom="density")

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

Notes: * Make your plots only in the training set + Don’t use the test set for exploration! * Things you should be looking for + imbalance in outcomes/predictors + outliers + groups of points not explained by a predictor + skewed variables

Basic preprocessing the predicator

library(caret)
library(kernlab);data(spam) # load the spam dataset

# create an indicator function.
inTrain <- createDataPartition(y=spam$type,p=0.75, list=FALSE) # split the data set in to 75% training

training <- spam[inTrain,]
testing <- spam[-inTrain,]

hist(training$capitalAve, main="", xlab="ave. capital run length")

mean(training$capitalAve)

## [1] 5.452347

sd(training$capitalAve)

## [1] 32.04618

# we found that variable is skewed and highly variable

# standardizing

trainCapAve <- training$capitalAve
trainCapAveS <- (trainCapAve - mean(trainCapAve))/sd(trainCapAve)
mean(trainCapAveS)

## [1] 3.3215e-16

sd(trainCapAveS)

## [1] 1

# standardizing -test
testCapAve <- testing$capitalAve
testCapAveS <-(testCapAve - mean(trainCapAve))/sd(trainCapAve)
mean(testCapAveS)

## [1] -0.0325641

sd(testCapAveS)

## [1] 0.9598581

# standardizing - preProcess function (built in caret)
preObj <- preProcess(training[,-58], method = c("center","scale")) # center every variable and scale every variable except for the outcome variable

trainCapAveS <- predict(preObj, training[,-58])$capitalAve
mean(trainCapAveS)

## [1] 3.3215e-16

sd(trainCapAveS)

## [1] 1

# apply the same preproces to the testset!

testCapAveS <- predict(preObj, testing[,-58])$capitalAve
mean(testCapAveS)

## [1] -0.0325641

sd(testCapAveS)

## [1] 0.9598581

# you can pas the preProcess in the train as an argument
modelFit <- train(type~., data=training, preProcess=c("center","scale"), method="glm")

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: algorithm did not converge

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

modelFit

## Generalized Linear Model 
## 
## 3451 samples
##   57 predictor
##    2 classes: 'nonspam', 'spam' 
## 
## Pre-processing: centered (57), scaled (57) 
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 3451, 3451, 3451, 3451, 3451, 3451, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.9194936  0.8308233

# another way to standare variable
# standardizing - Box-Cox transforms

preObj <- preProcess(training[,-58], method=c("BoxCox"))
trainCapAveS <- predict(preObj, training[,-58])$capitalAve
par(mfrow=c(1,2)); 
hist(trainCapAveS); qqnorm(trainCapAveS)

# fill the missing data.
set.seed(13343)

# make some values NA
training$capAve <- training$capitalAve
selectNA <- rbinom(dim(training)[1], size=1,prob=0.05)==1
training$capAve[selectNA]<-NA

# impute and Standardize
# install.packages("RANN")
library(RANN)


preObj <- preProcess(training[,-58], method="knnImpute")
capAve <-predict(preObj, training[,-58])$capAve

# Standardize true values
capAveTruth <- training$capitalAve
capAveTruth <- (capAveTruth-mean(capAveTruth))/sd(capAveTruth)

quantile(capAve-capAveTruth) # compare imputed and actual

##           0%          25%          50%          75%         100% 
## -1.522799841  0.001799650  0.002202549  0.002389961  0.708600118

Notes and further reading

Training and test must be preocssed in the same way test transformations will likely be imperfect + especially if the test/training sets collected at different times careful when transforming factor variables*

Covariate creation

Two levels of covariate creation

• Level 1: From raw data to covariate
• Level 2 : transforming tidy covariates

# Load example data
library(ISLR); library(caret); data(Wage);
inTrain <- createDataPartition(y=Wage$wage, p=0.7, list=F)
training <- Wage[inTrain,]; testing <- Wage[-inTrain,]


# Common covariates to add, dummy variables
table(training$jobclass)

## 
##  1. Industrial 2. Information 
##           1069           1033

# convert factor variables to indicator variables

dummies <- dummyVars(wage ~ jobclass, data=training)
head(predict(dummies, newdata=training))

##        jobclass.1. Industrial jobclass.2. Information
## 231655                      1                       0
## 86582                       0                       1
## 161300                      1                       0
## 155159                      0                       1
## 376662                      0                       1
## 450601                      1                       0

# Removing zero covariates (some variable, no variablility)
nsv <- nearZeroVar(training, saveMetrics = T)
nsv

##            freqRatio percentUnique zeroVar   nzv
## year        1.034384    0.33301618   FALSE FALSE
## age         1.116883    2.90199810   FALSE FALSE
## maritl      3.374713    0.23786870   FALSE FALSE
## race        8.146226    0.19029496   FALSE FALSE
## education   1.438525    0.23786870   FALSE FALSE
## region      0.000000    0.04757374    TRUE  TRUE
## jobclass    1.034850    0.09514748   FALSE FALSE
## health      2.480132    0.09514748   FALSE FALSE
## health_ins  2.199391    0.09514748   FALSE FALSE
## logwage     1.133333   19.12464320   FALSE FALSE
## wage        1.133333   19.12464320   FALSE FALSE

# So this is a nice way to throw those sort of less meaningful predictors out right away.

Spline basis

# install.packages("splines")
library(splines)
bsBasis <- bs(training$age, df=3)
bsBasis

##                   1            2            3
##    [1,] 0.000000000 0.0000000000 0.000000e+00
##    [2,] 0.236850055 0.0253767916 9.063140e-04
##    [3,] 0.416337988 0.3211750193 8.258786e-02
##    [4,] 0.430813836 0.2910904300 6.556091e-02
##    [5,] 0.306334128 0.4241549461 1.957638e-01
##    [6,] 0.424154946 0.3063341278 7.374710e-02
##    [7,] 0.377630828 0.0906313987 7.250512e-03
##    [8,] 0.440355309 0.2596967205 5.105149e-02
##    [9,] 0.335537578 0.4074384881 1.649156e-01
##   [10,] 0.416337988 0.3211750193 8.258786e-02
##   [11,] 0.433331375 0.1637029640 2.061445e-02
##   [12,] 0.444358195 0.2275981001 3.885821e-02
##   [13,] 0.306334128 0.4241549461 1.957638e-01
##   [14,] 0.442218287 0.1953987782 2.877966e-02
##   [15,] 0.275519452 0.4362391326 2.302373e-01
##   [16,] 0.444093854 0.2114732637 3.356718e-02
##   [17,] 0.443086838 0.2436977611 4.467792e-02
##   [18,] 0.443086838 0.2436977611 4.467792e-02
##   [19,] 0.444093854 0.2114732637 3.356718e-02
##   [20,] 0.375000000 0.3750000000 1.250000e-01
##   [21,] 0.430813836 0.2910904300 6.556091e-02
##   [22,] 0.426168977 0.1482326877 1.718640e-02
##   [23,] 0.259696720 0.4403553087 2.488965e-01
##   [24,] 0.000000000 0.0000000000 0.000000e+00
##   [25,] 0.291090430 0.4308138364 2.125348e-01
##   [26,] 0.417093250 0.1331148669 1.416116e-02
##   [27,] 0.438655970 0.1794501695 2.447048e-02
##   [28,] 0.275519452 0.4362391326 2.302373e-01
##   [29,] 0.065456010 0.3403712531 5.899768e-01
##   [30,] 0.266544426 0.0339238361 1.439193e-03
##   [31,] 0.406028666 0.1184250277 1.151354e-02
##   [32,] 0.430813836 0.2910904300 6.556091e-02
##   [33,] 0.444358195 0.2275981001 3.885821e-02
##   [34,] 0.335537578 0.4074384881 1.649156e-01
##   [35,] 0.266544426 0.0339238361 1.439193e-03
##   [36,] 0.417093250 0.1331148669 1.416116e-02
##   [37,] 0.259696720 0.4403553087 2.488965e-01
##   [38,] 0.054038972 0.3182294988 6.246727e-01
##   [39,] 0.204487093 0.0179374643 5.244873e-04
##   [40,] 0.377630828 0.0906313987 7.250512e-03
##   [41,] 0.169380014 0.0116813803 2.685375e-04
##   [42,] 0.227598100 0.4443581954 2.891855e-01
##   [43,] 0.340371253 0.0654560102 4.195898e-03
##   [44,] 0.195398778 0.4422182874 3.336033e-01
##   [45,] 0.426168977 0.1482326877 1.718640e-02
##   [46,] 0.430813836 0.2910904300 6.556091e-02
##   [47,] 0.306334128 0.4241549461 1.957638e-01
##   [48,] 0.386693968 0.3625255950 1.132892e-01
##   [49,] 0.375000000 0.3750000000 1.250000e-01
##   [50,] 0.436239133 0.2755194522 5.800410e-02
##   [51,] 0.291090430 0.4308138364 2.125348e-01
##   [52,] 0.131453291 0.0066840657 1.132892e-04
##   [53,] 0.243697761 0.4430868383 2.685375e-01
##   [54,] 0.392899701 0.1042386963 9.218388e-03
##   [55,] 0.266544426 0.0339238361 1.439193e-03
##   [56,] 0.406028666 0.1184250277 1.151354e-02
##   [57,] 0.424154946 0.3063341278 7.374710e-02
##   [58,] 0.211473264 0.4440938538 3.108657e-01
##   [59,] 0.424154946 0.3063341278 7.374710e-02
##   [60,] 0.291090430 0.4308138364 2.125348e-01
##   [61,] 0.266544426 0.0339238361 1.439193e-03
##   [62,] 0.321175019 0.4163379880 1.798991e-01
##   [63,] 0.065456010 0.3403712531 5.899768e-01
##   [64,] 0.397531973 0.3493462791 1.023338e-01
##   [65,] 0.426168977 0.1482326877 1.718640e-02
##   [66,] 0.169380014 0.0116813803 2.685375e-04
##   [67,] 0.416337988 0.3211750193 8.258786e-02
##   [68,] 0.430813836 0.2910904300 6.556091e-02
##   [69,] 0.417093250 0.1331148669 1.416116e-02
##   [70,] 0.179450170 0.4386559699 3.574234e-01
##   [71,] 0.442218287 0.1953987782 2.877966e-02
##   [72,] 0.362525595 0.3866939680 1.374912e-01
##   [73,] 0.440355309 0.2596967205 5.105149e-02
##   [74,] 0.444093854 0.2114732637 3.356718e-02
##   [75,] 0.433331375 0.1637029640 2.061445e-02
##   [76,] 0.360146521 0.0776786613 5.584740e-03
##   [77,] 0.444358195 0.2275981001 3.885821e-02
##   [78,] 0.291090430 0.4308138364 2.125348e-01
##   [79,] 0.444093854 0.2114732637 3.356718e-02
##   [80,] 0.375000000 0.3750000000 1.250000e-01
##   [81,] 0.436239133 0.2755194522 5.800410e-02
##   [82,] 0.430813836 0.2910904300 6.556091e-02
##   [83,] 0.444093854 0.2114732637 3.356718e-02
##   [84,] 0.259696720 0.4403553087 2.488965e-01
##   [85,] 0.266544426 0.0339238361 1.439193e-03
##   [86,] 0.375000000 0.3750000000 1.250000e-01
##   [87,] 0.440355309 0.2596967205 5.105149e-02
##   [88,] 0.375000000 0.3750000000 1.250000e-01
##   [89,] 0.335537578 0.4074384881 1.649156e-01
##   [90,] 0.430813836 0.2910904300 6.556091e-02
##   [91,] 0.211473264 0.4440938538 3.108657e-01
##   [92,] 0.407438488 0.3355375785 9.210835e-02
##   [93,] 0.131453291 0.0066840657 1.132892e-04
##   [94,] 0.195398778 0.4422182874 3.336033e-01
##   [95,] 0.406028666 0.1184250277 1.151354e-02
##   [96,] 0.293645732 0.0435030714 2.148300e-03
##   [97,] 0.406028666 0.1184250277 1.151354e-02
##   [98,] 0.442218287 0.1953987782 2.877966e-02
##   [99,] 0.169380014 0.0116813803 2.685375e-04
##  [100,] 0.424154946 0.3063341278 7.374710e-02
##  [101,] 0.433331375 0.1637029640 2.061445e-02
##  [102,] 0.443086838 0.2436977611 4.467792e-02
##  [103,] 0.433331375 0.1637029640 2.061445e-02
##  [104,] 0.433331375 0.1637029640 2.061445e-02
##  [105,] 0.430813836 0.2910904300 6.556091e-02
##  [106,] 0.417093250 0.1331148669 1.416116e-02
##  [107,] 0.211473264 0.4440938538 3.108657e-01
##  [108,] 0.444093854 0.2114732637 3.356718e-02
##  [109,] 0.321175019 0.4163379880 1.798991e-01
##  [110,] 0.259696720 0.4403553087 2.488965e-01
##  [111,] 0.148232688 0.4261689772 4.084119e-01
##  [112,] 0.433331375 0.1637029640 2.061445e-02
##  [113,] 0.306334128 0.4241549461 1.957638e-01
##  [114,] 0.416337988 0.3211750193 8.258786e-02
##  [115,] 0.386693968 0.3625255950 1.132892e-01
##  [116,] 0.407438488 0.3355375785 9.210835e-02
##  [117,] 0.291090430 0.4308138364 2.125348e-01
##  [118,] 0.375000000 0.3750000000 1.250000e-01
##  [119,] 0.426168977 0.1482326877 1.718640e-02
##  [120,] 0.443086838 0.2436977611 4.467792e-02
##  [121,] 0.442218287 0.1953987782 2.877966e-02
##  [122,] 0.444358195 0.2275981001 3.885821e-02
##  [123,] 0.335537578 0.4074384881 1.649156e-01
##  [124,] 0.362525595 0.3866939680 1.374912e-01
##  [125,] 0.397531973 0.3493462791 1.023338e-01
##  [126,] 0.318229499 0.0540389715 3.058810e-03
##  [127,] 0.424154946 0.3063341278 7.374710e-02
##  [128,] 0.442218287 0.1953987782 2.877966e-02
##  [129,] 0.335537578 0.4074384881 1.649156e-01
##  [130,] 0.444358195 0.2275981001 3.885821e-02
##  [131,] 0.392899701 0.1042386963 9.218388e-03
##  [132,] 0.243697761 0.4430868383 2.685375e-01
##  [133,] 0.377630828 0.0906313987 7.250512e-03
##  [134,] 0.318229499 0.0540389715 3.058810e-03
##  [135,] 0.433331375 0.1637029640 2.061445e-02
##  [136,] 0.386693968 0.3625255950 1.132892e-01
##  [137,] 0.360146521 0.0776786613 5.584740e-03
##  [138,] 0.266544426 0.0339238361 1.439193e-03
##  [139,] 0.443086838 0.2436977611 4.467792e-02
##  [140,] 0.318229499 0.0540389715 3.058810e-03
##  [141,] 0.375000000 0.3750000000 1.250000e-01
##  [142,] 0.169380014 0.0116813803 2.685375e-04
##  [143,] 0.416337988 0.3211750193 8.258786e-02
##  [144,] 0.163702964 0.4333313752 3.823512e-01
##  [145,] 0.375000000 0.3750000000 1.250000e-01
##  [146,] 0.266544426 0.0339238361 1.439193e-03
##  [147,] 0.360146521 0.0776786613 5.584740e-03
##  [148,] 0.442218287 0.1953987782 2.877966e-02
##  [149,] 0.433331375 0.1637029640 2.061445e-02
##  [150,] 0.407438488 0.3355375785 9.210835e-02
##  [151,] 0.243697761 0.4430868383 2.685375e-01
##  [152,] 0.444358195 0.2275981001 3.885821e-02
##  [153,] 0.442218287 0.1953987782 2.877966e-02
##  [154,] 0.318229499 0.0540389715 3.058810e-03
##  [155,] 0.442218287 0.1953987782 2.877966e-02
##  [156,] 0.275519452 0.4362391326 2.302373e-01
##  [157,] 0.438655970 0.1794501695 2.447048e-02
##  [158,] 0.204487093 0.0179374643 5.244873e-04
##  [159,] 0.407438488 0.3355375785 9.210835e-02
##  [160,] 0.306334128 0.4241549461 1.957638e-01
##  [161,] 0.179450170 0.4386559699 3.574234e-01
##  [162,] 0.443086838 0.2436977611 4.467792e-02
##  [163,] 0.321175019 0.4163379880 1.798991e-01
##  [164,] 0.204487093 0.0179374643 5.244873e-04
##  [165,] 0.426168977 0.1482326877 1.718640e-02
##  [166,] 0.430813836 0.2910904300 6.556091e-02
##  [167,] 0.227598100 0.4443581954 2.891855e-01
##  [168,] 0.211473264 0.4440938538 3.108657e-01
##  [169,] 0.375000000 0.3750000000 1.250000e-01
##  [170,] 0.416337988 0.3211750193 8.258786e-02
##  [171,] 0.169380014 0.0116813803 2.685375e-04
##  [172,] 0.438655970 0.1794501695 2.447048e-02
##  [173,] 0.444093854 0.2114732637 3.356718e-02
##  [174,] 0.397531973 0.3493462791 1.023338e-01
##  [175,] 0.433331375 0.1637029640 2.061445e-02
##  [176,] 0.375000000 0.3750000000 1.250000e-01
##  [177,] 0.443086838 0.2436977611 4.467792e-02
##  [178,] 0.406028666 0.1184250277 1.151354e-02
##  [179,] 0.259696720 0.4403553087 2.488965e-01
##  [180,] 0.033923836 0.2665444262 6.980925e-01
##  [181,] 0.375000000 0.3750000000 1.250000e-01
##  [182,] 0.377630828 0.0906313987 7.250512e-03
##  [183,] 0.360146521 0.0776786613 5.584740e-03
##  [184,] 0.444358195 0.2275981001 3.885821e-02
##  [185,] 0.436239133 0.2755194522 5.800410e-02
##  [186,] 0.386693968 0.3625255950 1.132892e-01
##  [187,] 0.424154946 0.3063341278 7.374710e-02
##  [188,] 0.406028666 0.1184250277 1.151354e-02
##  [189,] 0.407438488 0.3355375785 9.210835e-02
##  [190,] 0.335537578 0.4074384881 1.649156e-01
##  [191,] 0.169380014 0.0116813803 2.685375e-04
##  [192,] 0.321175019 0.4163379880 1.798991e-01
##  [193,] 0.426168977 0.1482326877 1.718640e-02
##  [194,] 0.444093854 0.2114732637 3.356718e-02
##  [195,] 0.436239133 0.2755194522 5.800410e-02
##  [196,] 0.266544426 0.0339238361 1.439193e-03
##  [197,] 0.360146521 0.0776786613 5.584740e-03
##  [198,] 0.340371253 0.0654560102 4.195898e-03
##  [199,] 0.407438488 0.3355375785 9.210835e-02
##  [200,] 0.275519452 0.4362391326 2.302373e-01
##  [201,] 0.440355309 0.2596967205 5.105149e-02
##  [202,] 0.195398778 0.4422182874 3.336033e-01
##  [203,] 0.397531973 0.3493462791 1.023338e-01
##  [204,] 0.318229499 0.0540389715 3.058810e-03
##  [205,] 0.243697761 0.4430868383 2.685375e-01
##  [206,] 0.318229499 0.0540389715 3.058810e-03
##  [207,] 0.335537578 0.4074384881 1.649156e-01
##  [208,] 0.416337988 0.3211750193 8.258786e-02
##  [209,] 0.266544426 0.0339238361 1.439193e-03
##  [210,] 0.440355309 0.2596967205 5.105149e-02
##  [211,] 0.306334128 0.4241549461 1.957638e-01
##  [212,] 0.204487093 0.0179374643 5.244873e-04
##  [213,] 0.392899701 0.1042386963 9.218388e-03
##  [214,] 0.335537578 0.4074384881 1.649156e-01
##  [215,] 0.416337988 0.3211750193 8.258786e-02
##  [216,] 0.443086838 0.2436977611 4.467792e-02
##  [217,] 0.417093250 0.1331148669 1.416116e-02
##  [218,] 0.266544426 0.0339238361 1.439193e-03
##  [219,] 0.236850055 0.0253767916 9.063140e-04
##  [220,] 0.236850055 0.0253767916 9.063140e-04
##  [221,] 0.440355309 0.2596967205 5.105149e-02
##  [222,] 0.436239133 0.2755194522 5.800410e-02
##  [223,] 0.291090430 0.4308138364 2.125348e-01
##  [224,] 0.211473264 0.4440938538 3.108657e-01
##  [225,] 0.443086838 0.2436977611 4.467792e-02
##  [226,] 0.440355309 0.2596967205 5.105149e-02
##  [227,] 0.000000000 0.0000000000 1.000000e+00
##  [228,] 0.321175019 0.4163379880 1.798991e-01
##  [229,] 0.443086838 0.2436977611 4.467792e-02
##  [230,] 0.433331375 0.1637029640 2.061445e-02
##  [231,] 0.236850055 0.0253767916 9.063140e-04
##  [232,] 0.377630828 0.0906313987 7.250512e-03
##  [233,] 0.090631399 0.3776308281 5.244873e-01
##  [234,] 0.306334128 0.4241549461 1.957638e-01
##  [235,] 0.318229499 0.0540389715 3.058810e-03
##  [236,] 0.321175019 0.4163379880 1.798991e-01
##  [237,] 0.386693968 0.3625255950 1.132892e-01
##  [238,] 0.227598100 0.4443581954 2.891855e-01
##  [239,] 0.416337988 0.3211750193 8.258786e-02
##  [240,] 0.430813836 0.2910904300 6.556091e-02
##  [241,] 0.377630828 0.0906313987 7.250512e-03
##  [242,] 0.259696720 0.4403553087 2.488965e-01
##  [243,] 0.321175019 0.4163379880 1.798991e-01
##  [244,] 0.436239133 0.2755194522 5.800410e-02
##  [245,] 0.204487093 0.0179374643 5.244873e-04
##  [246,] 0.243697761 0.4430868383 2.685375e-01
##  [247,] 0.430813836 0.2910904300 6.556091e-02
##  [248,] 0.417093250 0.1331148669 1.416116e-02
##  [249,] 0.275519452 0.4362391326 2.302373e-01
##  [250,] 0.442218287 0.1953987782 2.877966e-02
##  [251,] 0.440355309 0.2596967205 5.105149e-02
##  [252,] 0.417093250 0.1331148669 1.416116e-02
##  [253,] 0.362525595 0.3866939680 1.374912e-01
##  [254,] 0.321175019 0.4163379880 1.798991e-01
##  [255,] 0.442218287 0.1953987782 2.877966e-02
##  [256,] 0.090631399 0.0030210466 3.356718e-05
##  [257,] 0.293645732 0.0435030714 2.148300e-03
##  [258,] 0.360146521 0.0776786613 5.584740e-03
##  [259,] 0.397531973 0.3493462791 1.023338e-01
##  [260,] 0.306334128 0.4241549461 1.957638e-01
##  [261,] 0.204487093 0.0179374643 5.244873e-04
##  [262,] 0.430813836 0.2910904300 6.556091e-02
##  [263,] 0.386693968 0.3625255950 1.132892e-01
##  [264,] 0.417093250 0.1331148669 1.416116e-02
##  [265,] 0.335537578 0.4074384881 1.649156e-01
##  [266,] 0.349346279 0.3975319727 1.507880e-01
##  [267,] 0.397531973 0.3493462791 1.023338e-01
##  [268,] 0.340371253 0.0654560102 4.195898e-03
##  [269,] 0.335537578 0.4074384881 1.649156e-01
##  [270,] 0.204487093 0.0179374643 5.244873e-04
##  [271,] 0.133114867 0.4170932496 4.356307e-01
##  [272,] 0.318229499 0.0540389715 3.058810e-03
##  [273,] 0.417093250 0.1331148669 1.416116e-02
##  [274,] 0.375000000 0.3750000000 1.250000e-01
##  [275,] 0.318229499 0.0540389715 3.058810e-03
##  [276,] 0.443086838 0.2436977611 4.467792e-02
##  [277,] 0.407438488 0.3355375785 9.210835e-02
##  [278,] 0.321175019 0.4163379880 1.798991e-01
##  [279,] 0.266544426 0.0339238361 1.439193e-03
##  [280,] 0.433331375 0.1637029640 2.061445e-02
##  [281,] 0.362525595 0.3866939680 1.374912e-01
##  [282,] 0.426168977 0.1482326877 1.718640e-02
##  [283,] 0.386693968 0.3625255950 1.132892e-01
##  [284,] 0.375000000 0.3750000000 1.250000e-01
##  [285,] 0.440355309 0.2596967205 5.105149e-02
##  [286,] 0.442218287 0.1953987782 2.877966e-02
##  [287,] 0.243697761 0.4430868383 2.685375e-01
##  [288,] 0.340371253 0.0654560102 4.195898e-03
##  [289,] 0.417093250 0.1331148669 1.416116e-02
##  [290,] 0.362525595 0.3866939680 1.374912e-01
##  [291,] 0.444093854 0.2114732637 3.356718e-02
##  [292,] 0.375000000 0.3750000000 1.250000e-01
##  [293,] 0.424154946 0.3063341278 7.374710e-02
##  [294,] 0.362525595 0.3866939680 1.374912e-01
##  [295,] 0.416337988 0.3211750193 8.258786e-02
##  [296,] 0.424154946 0.3063341278 7.374710e-02
##  [297,] 0.227598100 0.4443581954 2.891855e-01
##  [298,] 0.349346279 0.3975319727 1.507880e-01
##  [299,] 0.416337988 0.3211750193 8.258786e-02
##  [300,] 0.417093250 0.1331148669 1.416116e-02
##  [301,] 0.416337988 0.3211750193 8.258786e-02
##  [302,] 0.362525595 0.3866939680 1.374912e-01
##  [303,] 0.444358195 0.2275981001 3.885821e-02
##  [304,] 0.375000000 0.3750000000 1.250000e-01
##  [305,] 0.090631399 0.0030210466 3.356718e-05
##  [306,] 0.392899701 0.1042386963 9.218388e-03
##  [307,] 0.375000000 0.3750000000 1.250000e-01
##  [308,] 0.275519452 0.4362391326 2.302373e-01
##  [309,] 0.195398778 0.4422182874 3.336033e-01
##  [310,] 0.275519452 0.4362391326 2.302373e-01
##  [311,] 0.349346279 0.3975319727 1.507880e-01
##  [312,] 0.436239133 0.2755194522 5.800410e-02
##  [313,] 0.416337988 0.3211750193 8.258786e-02
##  [314,] 0.377630828 0.0906313987 7.250512e-03
##  [315,] 0.386693968 0.3625255950 1.132892e-01
##  [316,] 0.417093250 0.1331148669 1.416116e-02
##  [317,] 0.392899701 0.1042386963 9.218388e-03
##  [318,] 0.386693968 0.3625255950 1.132892e-01
##  [319,] 0.433331375 0.1637029640 2.061445e-02
##  [320,] 0.397531973 0.3493462791 1.023338e-01
##  [321,] 0.416337988 0.3211750193 8.258786e-02
##  [322,] 0.335537578 0.4074384881 1.649156e-01
##  [323,] 0.375000000 0.3750000000 1.250000e-01
##  [324,] 0.407438488 0.3355375785 9.210835e-02
##  [325,] 0.430813836 0.2910904300 6.556091e-02
##  [326,] 0.424154946 0.3063341278 7.374710e-02
##  [327,] 0.443086838 0.2436977611 4.467792e-02
##  [328,] 0.417093250 0.1331148669 1.416116e-02
##  [329,] 0.444093854 0.2114732637 3.356718e-02
##  [330,] 0.440355309 0.2596967205 5.105149e-02
##  [331,] 0.377630828 0.0906313987 7.250512e-03
##  [332,] 0.349346279 0.3975319727 1.507880e-01
##  [333,] 0.444358195 0.2275981001 3.885821e-02
##  [334,] 0.433331375 0.1637029640 2.061445e-02
##  [335,] 0.397531973 0.3493462791 1.023338e-01
##  [336,] 0.349346279 0.3975319727 1.507880e-01
##  [337,] 0.440355309 0.2596967205 5.105149e-02
##  [338,] 0.163702964 0.4333313752 3.823512e-01
##  [339,] 0.195398778 0.4422182874 3.336033e-01
##  [340,] 0.407438488 0.3355375785 9.210835e-02
##  [341,] 0.204487093 0.0179374643 5.244873e-04
##  [342,] 0.416337988 0.3211750193 8.258786e-02
##  [343,] 0.163702964 0.4333313752 3.823512e-01
##  [344,] 0.227598100 0.4443581954 2.891855e-01
##  [345,] 0.377630828 0.0906313987 7.250512e-03
##  [346,] 0.416337988 0.3211750193 8.258786e-02
##  [347,] 0.436239133 0.2755194522 5.800410e-02
##  [348,] 0.335537578 0.4074384881 1.649156e-01
##  [349,] 0.306334128 0.4241549461 1.957638e-01
##  [350,] 0.377630828 0.0906313987 7.250512e-03
##  [351,] 0.444093854 0.2114732637 3.356718e-02
##  [352,] 0.444358195 0.2275981001 3.885821e-02
##  [353,] 0.362525595 0.3866939680 1.374912e-01
##  [354,] 0.397531973 0.3493462791 1.023338e-01
##  [355,] 0.416337988 0.3211750193 8.258786e-02
##  [356,] 0.424154946 0.3063341278 7.374710e-02
##  [357,] 0.335537578 0.4074384881 1.649156e-01
##  [358,] 0.436239133 0.2755194522 5.800410e-02
##  [359,] 0.275519452 0.4362391326 2.302373e-01
##  [360,] 0.362525595 0.3866939680 1.374912e-01
##  [361,] 0.321175019 0.4163379880 1.798991e-01
##  [362,] 0.318229499 0.0540389715 3.058810e-03
##  [363,] 0.275519452 0.4362391326 2.302373e-01
##  [364,] 0.362525595 0.3866939680 1.374912e-01
##  [365,] 0.362525595 0.3866939680 1.374912e-01
##  [366,] 0.375000000 0.3750000000 1.250000e-01
##  [367,] 0.436239133 0.2755194522 5.800410e-02
##  [368,] 0.362525595 0.3866939680 1.374912e-01
##  [369,] 0.321175019 0.4163379880 1.798991e-01
##  [370,] 0.340371253 0.0654560102 4.195898e-03
##  [371,] 0.236850055 0.0253767916 9.063140e-04
##  [372,] 0.266544426 0.0339238361 1.439193e-03
##  [373,] 0.444093854 0.2114732637 3.356718e-02
##  [374,] 0.397531973 0.3493462791 1.023338e-01
##  [375,] 0.444093854 0.2114732637 3.356718e-02
##  [376,] 0.444358195 0.2275981001 3.885821e-02
##  [377,] 0.335537578 0.4074384881 1.649156e-01
##  [378,] 0.195398778 0.4422182874 3.336033e-01
##  [379,] 0.195398778 0.4422182874 3.336033e-01
##  [380,] 0.318229499 0.0540389715 3.058810e-03
##  [381,] 0.416337988 0.3211750193 8.258786e-02
##  [382,] 0.243697761 0.4430868383 2.685375e-01
##  [383,] 0.426168977 0.1482326877 1.718640e-02
##  [384,] 0.443086838 0.2436977611 4.467792e-02
##  [385,] 0.349346279 0.3975319727 1.507880e-01
##  [386,] 0.362525595 0.3866939680 1.374912e-01
##  [387,] 0.148232688 0.4261689772 4.084119e-01
##  [388,] 0.306334128 0.4241549461 1.957638e-01
##  [389,] 0.436239133 0.2755194522 5.800410e-02
##  [390,] 0.392899701 0.1042386963 9.218388e-03
##  [391,] 0.406028666 0.1184250277 1.151354e-02
##  [392,] 0.349346279 0.3975319727 1.507880e-01
##  [393,] 0.017937464 0.2044870934 7.770510e-01
##  [394,] 0.340371253 0.0654560102 4.195898e-03
##  [395,] 0.340371253 0.0654560102 4.195898e-03
##  [396,] 0.406028666 0.1184250277 1.151354e-02
##  [397,] 0.321175019 0.4163379880 1.798991e-01
##  [398,] 0.438655970 0.1794501695 2.447048e-02
##  [399,] 0.430813836 0.2910904300 6.556091e-02
##  [400,] 0.349346279 0.3975319727 1.507880e-01
##  [401,] 0.444358195 0.2275981001 3.885821e-02
##  [402,] 0.227598100 0.4443581954 2.891855e-01
##  [403,] 0.204487093 0.0179374643 5.244873e-04
##  [404,] 0.443086838 0.2436977611 4.467792e-02
##  [405,] 0.266544426 0.0339238361 1.439193e-03
##  [406,] 0.397531973 0.3493462791 1.023338e-01
##  [407,] 0.335537578 0.4074384881 1.649156e-01
##  [408,] 0.417093250 0.1331148669 1.416116e-02
##  [409,] 0.442218287 0.1953987782 2.877966e-02
##  [410,] 0.426168977 0.1482326877 1.718640e-02
##  [411,] 0.349346279 0.3975319727 1.507880e-01
##  [412,] 0.362525595 0.3866939680 1.374912e-01
##  [413,] 0.148232688 0.4261689772 4.084119e-01
##  [414,] 0.306334128 0.4241549461 1.957638e-01
##  [415,] 0.362525595 0.3866939680 1.374912e-01
##  [416,] 0.406028666 0.1184250277 1.151354e-02
##  [417,] 0.442218287 0.1953987782 2.877966e-02
##  [418,] 0.046838810 0.0007678494 4.195898e-06
##  [419,] 0.436239133 0.2755194522 5.800410e-02
##  [420,] 0.293645732 0.0435030714 2.148300e-03
##  [421,] 0.407438488 0.3355375785 9.210835e-02
##  [422,] 0.000000000 0.0000000000 0.000000e+00
##  [423,] 0.430813836 0.2910904300 6.556091e-02
##  [424,] 0.179450170 0.4386559699 3.574234e-01
##  [425,] 0.443086838 0.2436977611 4.467792e-02
##  [426,] 0.406028666 0.1184250277 1.151354e-02
##  [427,] 0.386693968 0.3625255950 1.132892e-01
##  [428,] 0.433331375 0.1637029640 2.061445e-02
##  [429,] 0.397531973 0.3493462791 1.023338e-01
##  [430,] 0.291090430 0.4308138364 2.125348e-01
##  [431,] 0.335537578 0.4074384881 1.649156e-01
##  [432,] 0.318229499 0.0540389715 3.058810e-03
##  [433,] 0.169380014 0.0116813803 2.685375e-04
##  [434,] 0.436239133 0.2755194522 5.800410e-02
##  [435,] 0.360146521 0.0776786613 5.584740e-03
##  [436,] 0.392899701 0.1042386963 9.218388e-03
##  [437,] 0.227598100 0.4443581954 2.891855e-01
##  [438,] 0.438655970 0.1794501695 2.447048e-02
##  [439,] 0.406028666 0.1184250277 1.151354e-02
##  [440,] 0.406028666 0.1184250277 1.151354e-02
##  [441,] 0.266544426 0.0339238361 1.439193e-03
##  [442,] 0.430813836 0.2910904300 6.556091e-02
##  [443,] 0.259696720 0.4403553087 2.488965e-01
##  [444,] 0.375000000 0.3750000000 1.250000e-01
##  [445,] 0.440355309 0.2596967205 5.105149e-02
##  [446,] 0.211473264 0.4440938538 3.108657e-01
##  [447,] 0.275519452 0.4362391326 2.302373e-01
##  [448,] 0.318229499 0.0540389715 3.058810e-03
##  [449,] 0.397531973 0.3493462791 1.023338e-01
##  [450,] 0.440355309 0.2596967205 5.105149e-02
##  [451,] 0.360146521 0.0776786613 5.584740e-03
##  [452,] 0.436239133 0.2755194522 5.800410e-02
##  [453,] 0.349346279 0.3975319727 1.507880e-01
##  [454,] 0.397531973 0.3493462791 1.023338e-01
##  [455,] 0.392899701 0.1042386963 9.218388e-03
##  [456,] 0.227598100 0.4443581954 2.891855e-01
##  [457,] 0.436239133 0.2755194522 5.800410e-02
##  [458,] 0.433331375 0.1637029640 2.061445e-02
##  [459,] 0.444093854 0.2114732637 3.356718e-02
##  [460,] 0.416337988 0.3211750193 8.258786e-02
##  [461,] 0.243697761 0.4430868383 2.685375e-01
##  [462,] 0.293645732 0.0435030714 2.148300e-03
##  [463,] 0.377630828 0.0906313987 7.250512e-03
##  [464,] 0.444093854 0.2114732637 3.356718e-02
##  [465,] 0.335537578 0.4074384881 1.649156e-01
##  [466,] 0.321175019 0.4163379880 1.798991e-01
##  [467,] 0.335537578 0.4074384881 1.649156e-01
##  [468,] 0.318229499 0.0540389715 3.058810e-03
##  [469,] 0.406028666 0.1184250277 1.151354e-02
##  [470,] 0.430813836 0.2910904300 6.556091e-02
##  [471,] 0.362525595 0.3866939680 1.374912e-01
##  [472,] 0.321175019 0.4163379880 1.798991e-01
##  [473,] 0.306334128 0.4241549461 1.957638e-01
##  [474,] 0.236850055 0.0253767916 9.063140e-04
##  [475,] 0.443086838 0.2436977611 4.467792e-02
##  [476,] 0.377630828 0.0906313987 7.250512e-03
##  [477,] 0.291090430 0.4308138364 2.125348e-01
##  [478,] 0.416337988 0.3211750193 8.258786e-02
##  [479,] 0.424154946 0.3063341278 7.374710e-02
##  [480,] 0.442218287 0.1953987782 2.877966e-02
##  [481,] 0.424154946 0.3063341278 7.374710e-02
##  [482,] 0.335537578 0.4074384881 1.649156e-01
##  [483,] 0.291090430 0.4308138364 2.125348e-01
##  [484,] 0.430813836 0.2910904300 6.556091e-02
##  [485,] 0.318229499 0.0540389715 3.058810e-03
##  [486,] 0.430813836 0.2910904300 6.556091e-02
##  [487,] 0.377630828 0.0906313987 7.250512e-03
##  [488,] 0.430813836 0.2910904300 6.556091e-02
##  [489,] 0.386693968 0.3625255950 1.132892e-01
##  [490,] 0.417093250 0.1331148669 1.416116e-02
##  [491,] 0.362525595 0.3866939680 1.374912e-01
##  [492,] 0.375000000 0.3750000000 1.250000e-01
##  [493,] 0.236850055 0.0253767916 9.063140e-04
##  [494,] 0.424154946 0.3063341278 7.374710e-02
##  [495,] 0.417093250 0.1331148669 1.416116e-02
##  [496,] 0.386693968 0.3625255950 1.132892e-01
##  [497,] 0.275519452 0.4362391326 2.302373e-01
##  [498,] 0.424154946 0.3063341278 7.374710e-02
##  [499,] 0.318229499 0.0540389715 3.058810e-03
##  [500,] 0.243697761 0.4430868383 2.685375e-01
##  [501,] 0.335537578 0.4074384881 1.649156e-01
##  [502,] 0.349346279 0.3975319727 1.507880e-01
##  [503,] 0.392899701 0.1042386963 9.218388e-03
##  [504,] 0.416337988 0.3211750193 8.258786e-02
##  [505,] 0.430813836 0.2910904300 6.556091e-02
##  [506,] 0.407438488 0.3355375785 9.210835e-02
##  [507,] 0.349346279 0.3975319727 1.507880e-01
##  [508,] 0.335537578 0.4074384881 1.649156e-01
##  [509,] 0.443086838 0.2436977611 4.467792e-02
##  [510,] 0.293645732 0.0435030714 2.148300e-03
##  [511,] 0.375000000 0.3750000000 1.250000e-01
##  [512,] 0.444093854 0.2114732637 3.356718e-02
##  [513,] 0.362525595 0.3866939680 1.374912e-01
##  [514,] 0.163702964 0.4333313752 3.823512e-01
##  [515,] 0.433331375 0.1637029640 2.061445e-02
##  [516,] 0.417093250 0.1331148669 1.416116e-02
##  [517,] 0.360146521 0.0776786613 5.584740e-03
##  [518,] 0.179450170 0.4386559699 3.574234e-01
##  [519,] 0.243697761 0.4430868383 2.685375e-01
##  [520,] 0.444358195 0.2275981001 3.885821e-02
##  [521,] 0.236850055 0.0253767916 9.063140e-04
##  [522,] 0.195398778 0.4422182874 3.336033e-01
##  [523,] 0.243697761 0.4430868383 2.685375e-01
##  [524,] 0.397531973 0.3493462791 1.023338e-01
##  [525,] 0.444093854 0.2114732637 3.356718e-02
##  [526,] 0.392899701 0.1042386963 9.218388e-03
##  [527,] 0.275519452 0.4362391326 2.302373e-01
##  [528,] 0.424154946 0.3063341278 7.374710e-02
##  [529,] 0.392899701 0.1042386963 9.218388e-03
##  [530,] 0.291090430 0.4308138364 2.125348e-01
##  [531,] 0.362525595 0.3866939680 1.374912e-01
##  [532,] 0.266544426 0.0339238361 1.439193e-03
##  [533,] 0.291090430 0.4308138364 2.125348e-01
##  [534,] 0.340371253 0.0654560102 4.195898e-03
##  [535,] 0.377630828 0.0906313987 7.250512e-03
##  [536,] 0.407438488 0.3355375785 9.210835e-02
##  [537,] 0.204487093 0.0179374643 5.244873e-04
##  [538,] 0.211473264 0.4440938538 3.108657e-01
##  [539,] 0.416337988 0.3211750193 8.258786e-02
##  [540,] 0.417093250 0.1331148669 1.416116e-02
##  [541,] 0.243697761 0.4430868383 2.685375e-01
##  [542,] 0.236850055 0.0253767916 9.063140e-04
##  [543,] 0.275519452 0.4362391326 2.302373e-01
##  [544,] 0.275519452 0.4362391326 2.302373e-01
##  [545,] 0.275519452 0.4362391326 2.302373e-01
##  [546,] 0.416337988 0.3211750193 8.258786e-02
##  [547,] 0.243697761 0.4430868383 2.685375e-01
##  [548,] 0.377630828 0.0906313987 7.250512e-03
##  [549,] 0.407438488 0.3355375785 9.210835e-02
##  [550,] 0.386693968 0.3625255950 1.132892e-01
##  [551,] 0.392899701 0.1042386963 9.218388e-03
##  [552,] 0.306334128 0.4241549461 1.957638e-01
##  [553,] 0.335537578 0.4074384881 1.649156e-01
##  [554,] 0.065456010 0.3403712531 5.899768e-01
##  [555,] 0.424154946 0.3063341278 7.374710e-02
##  [556,] 0.426168977 0.1482326877 1.718640e-02
##  [557,] 0.340371253 0.0654560102 4.195898e-03
##  [558,] 0.444358195 0.2275981001 3.885821e-02
##  [559,] 0.335537578 0.4074384881 1.649156e-01
##  [560,] 0.426168977 0.1482326877 1.718640e-02
##  [561,] 0.417093250 0.1331148669 1.416116e-02
##  [562,] 0.416337988 0.3211750193 8.258786e-02
##  [563,] 0.243697761 0.4430868383 2.685375e-01
##  [564,] 0.163702964 0.4333313752 3.823512e-01
##  [565,] 0.321175019 0.4163379880 1.798991e-01
##  [566,] 0.131453291 0.0066840657 1.132892e-04
##  [567,] 0.444093854 0.2114732637 3.356718e-02
##  [568,] 0.000000000 0.0000000000 0.000000e+00
##  [569,] 0.340371253 0.0654560102 4.195898e-03
##  [570,] 0.417093250 0.1331148669 1.416116e-02
##  [571,] 0.406028666 0.1184250277 1.151354e-02
##  [572,] 0.340371253 0.0654560102 4.195898e-03
##  [573,] 0.397531973 0.3493462791 1.023338e-01
##  [574,] 0.321175019 0.4163379880 1.798991e-01
##  [575,] 0.386693968 0.3625255950 1.132892e-01
##  [576,] 0.438655970 0.1794501695 2.447048e-02
##  [577,] 0.090631399 0.3776308281 5.244873e-01
##  [578,] 0.133114867 0.4170932496 4.356307e-01
##  [579,] 0.443086838 0.2436977611 4.467792e-02
##  [580,] 0.438655970 0.1794501695 2.447048e-02
##  [581,] 0.442218287 0.1953987782 2.877966e-02
##  [582,] 0.236850055 0.0253767916 9.063140e-04
##  [583,] 0.118425028 0.4060286664 4.640328e-01
##  [584,] 0.417093250 0.1331148669 1.416116e-02
##  [585,] 0.424154946 0.3063341278 7.374710e-02
##  [586,] 0.386693968 0.3625255950 1.132892e-01
##  [587,] 0.397531973 0.3493462791 1.023338e-01
##  [588,] 0.440355309 0.2596967205 5.105149e-02
##  [589,] 0.291090430 0.4308138364 2.125348e-01
##  [590,] 0.417093250 0.1331148669 1.416116e-02
##  [591,] 0.275519452 0.4362391326 2.302373e-01
##  [592,] 0.360146521 0.0776786613 5.584740e-03
##  [593,] 0.397531973 0.3493462791 1.023338e-01
##  [594,] 0.416337988 0.3211750193 8.258786e-02
##  [595,] 0.266544426 0.0339238361 1.439193e-03
##  [596,] 0.416337988 0.3211750193 8.258786e-02
##  [597,] 0.443086838 0.2436977611 4.467792e-02
##  [598,] 0.275519452 0.4362391326 2.302373e-01
##  [599,] 0.444358195 0.2275981001 3.885821e-02
##  [600,] 0.291090430 0.4308138364 2.125348e-01
##  [601,] 0.195398778 0.4422182874 3.336033e-01
##  [602,] 0.444358195 0.2275981001 3.885821e-02
##  [603,] 0.377630828 0.0906313987 7.250512e-03
##  [604,] 0.417093250 0.1331148669 1.416116e-02
##  [605,] 0.433331375 0.1637029640 2.061445e-02
##  [606,] 0.442218287 0.1953987782 2.877966e-02
##  [607,] 0.417093250 0.1331148669 1.416116e-02
##  [608,] 0.386693968 0.3625255950 1.132892e-01
##  [609,] 0.397531973 0.3493462791 1.023338e-01
##  [610,] 0.211473264 0.4440938538 3.108657e-01
##  [611,] 0.340371253 0.0654560102 4.195898e-03
##  [612,] 0.340371253 0.0654560102 4.195898e-03
##  [613,] 0.386693968 0.3625255950 1.132892e-01
##  [614,] 0.360146521 0.0776786613 5.584740e-03
##  [615,] 0.443086838 0.2436977611 4.467792e-02
##  [616,] 0.406028666 0.1184250277 1.151354e-02
##  [617,] 0.443086838 0.2436977611 4.467792e-02
##  [618,] 0.436239133 0.2755194522 5.800410e-02
##  [619,] 0.438655970 0.1794501695 2.447048e-02
##  [620,] 0.444358195 0.2275981001 3.885821e-02
##  [621,] 0.424154946 0.3063341278 7.374710e-02
##  [622,] 0.430813836 0.2910904300 6.556091e-02
##  [623,] 0.424154946 0.3063341278 7.374710e-02
##  [624,] 0.360146521 0.0776786613 5.584740e-03
##  [625,] 0.375000000 0.3750000000 1.250000e-01
##  [626,] 0.407438488 0.3355375785 9.210835e-02
##  [627,] 0.440355309 0.2596967205 5.105149e-02
##  [628,] 0.335537578 0.4074384881 1.649156e-01
##  [629,] 0.430813836 0.2910904300 6.556091e-02
##  [630,] 0.444093854 0.2114732637 3.356718e-02
##  [631,] 0.436239133 0.2755194522 5.800410e-02
##  [632,] 0.275519452 0.4362391326 2.302373e-01
##  [633,] 0.444358195 0.2275981001 3.885821e-02
##  [634,] 0.417093250 0.1331148669 1.416116e-02
##  [635,] 0.417093250 0.1331148669 1.416116e-02
##  [636,] 0.440355309 0.2596967205 5.105149e-02
##  [637,] 0.424154946 0.3063341278 7.374710e-02
##  [638,] 0.416337988 0.3211750193 8.258786e-02
##  [639,] 0.360146521 0.0776786613 5.584740e-03
##  [640,] 0.436239133 0.2755194522 5.800410e-02
##  [641,] 0.090631399 0.3776308281 5.244873e-01
##  [642,] 0.397531973 0.3493462791 1.023338e-01
##  [643,] 0.377630828 0.0906313987 7.250512e-03
##  [644,] 0.375000000 0.3750000000 1.250000e-01
##  [645,] 0.438655970 0.1794501695 2.447048e-02
##  [646,] 0.424154946 0.3063341278 7.374710e-02
##  [647,] 0.306334128 0.4241549461 1.957638e-01
##  [648,] 0.436239133 0.2755194522 5.800410e-02
##  [649,] 0.444358195 0.2275981001 3.885821e-02
##  [650,] 0.377630828 0.0906313987 7.250512e-03
##  [651,] 0.417093250 0.1331148669 1.416116e-02
##  [652,] 0.340371253 0.0654560102 4.195898e-03
##  [653,] 0.444093854 0.2114732637 3.356718e-02
##  [654,] 0.377630828 0.0906313987 7.250512e-03
##  [655,] 0.266544426 0.0339238361 1.439193e-03
##  [656,] 0.293645732 0.0435030714 2.148300e-03
##  [657,] 0.179450170 0.4386559699 3.574234e-01
##  [658,] 0.406028666 0.1184250277 1.151354e-02
##  [659,] 0.443086838 0.2436977611 4.467792e-02
##  [660,] 0.375000000 0.3750000000 1.250000e-01
##  [661,] 0.407438488 0.3355375785 9.210835e-02
##  [662,] 0.436239133 0.2755194522 5.800410e-02
##  [663,] 0.243697761 0.4430868383 2.685375e-01
##  [664,] 0.377630828 0.0906313987 7.250512e-03
##  [665,] 0.318229499 0.0540389715 3.058810e-03
##  [666,] 0.291090430 0.4308138364 2.125348e-01
##  [667,] 0.362525595 0.3866939680 1.374912e-01
##  [668,] 0.291090430 0.4308138364 2.125348e-01
##  [669,] 0.443086838 0.2436977611 4.467792e-02
##  [670,] 0.406028666 0.1184250277 1.151354e-02
##  [671,] 0.318229499 0.0540389715 3.058810e-03
##  [672,] 0.375000000 0.3750000000 1.250000e-01
##  [673,] 0.362525595 0.3866939680 1.374912e-01
##  [674,] 0.259696720 0.4403553087 2.488965e-01
##  [675,] 0.043503071 0.2936457319 6.607029e-01
##  [676,] 0.438655970 0.1794501695 2.447048e-02
##  [677,] 0.163702964 0.4333313752 3.823512e-01
##  [678,] 0.407438488 0.3355375785 9.210835e-02
##  [679,] 0.291090430 0.4308138364 2.125348e-01
##  [680,] 0.424154946 0.3063341278 7.374710e-02
##  [681,] 0.424154946 0.3063341278 7.374710e-02
##  [682,] 0.406028666 0.1184250277 1.151354e-02
##  [683,] 0.211473264 0.4440938538 3.108657e-01
##  [684,] 0.436239133 0.2755194522 5.800410e-02
##  [685,] 0.392899701 0.1042386963 9.218388e-03
##  [686,] 0.306334128 0.4241549461 1.957638e-01
##  [687,] 0.407438488 0.3355375785 9.210835e-02
##  [688,] 0.362525595 0.3866939680 1.374912e-01
##  [689,] 0.417093250 0.1331148669 1.416116e-02
##  [690,] 0.426168977 0.1482326877 1.718640e-02
##  [691,] 0.349346279 0.3975319727 1.507880e-01
##  [692,] 0.417093250 0.1331148669 1.416116e-02
##  [693,] 0.227598100 0.4443581954 2.891855e-01
##  [694,] 0.340371253 0.0654560102 4.195898e-03
##  [695,] 0.443086838 0.2436977611 4.467792e-02
##  [696,] 0.360146521 0.0776786613 5.584740e-03
##  [697,] 0.426168977 0.1482326877 1.718640e-02
##  [698,] 0.266544426 0.0339238361 1.439193e-03
##  [699,] 0.118425028 0.4060286664 4.640328e-01
##  [700,] 0.430813836 0.2910904300 6.556091e-02
##  [701,] 0.416337988 0.3211750193 8.258786e-02
##  [702,] 0.433331375 0.1637029640 2.061445e-02
##  [703,] 0.430813836 0.2910904300 6.556091e-02
##  [704,] 0.375000000 0.3750000000 1.250000e-01
##  [705,] 0.211473264 0.4440938538 3.108657e-01
##  [706,] 0.291090430 0.4308138364 2.125348e-01
##  [707,] 0.406028666 0.1184250277 1.151354e-02
##  [708,] 0.321175019 0.4163379880 1.798991e-01
##  [709,] 0.259696720 0.4403553087 2.488965e-01
##  [710,] 0.227598100 0.4443581954 2.891855e-01
##  [711,] 0.275519452 0.4362391326 2.302373e-01
##  [712,] 0.211473264 0.4440938538 3.108657e-01
##  [713,] 0.386693968 0.3625255950 1.132892e-01
##  [714,] 0.444358195 0.2275981001 3.885821e-02
##  [715,] 0.406028666 0.1184250277 1.151354e-02
##  [716,] 0.349346279 0.3975319727 1.507880e-01
##  [717,] 0.397531973 0.3493462791 1.023338e-01
##  [718,] 0.424154946 0.3063341278 7.374710e-02
##  [719,] 0.407438488 0.3355375785 9.210835e-02
##  [720,] 0.236850055 0.0253767916 9.063140e-04
##  [721,] 0.442218287 0.1953987782 2.877966e-02
##  [722,] 0.392899701 0.1042386963 9.218388e-03
##  [723,] 0.043503071 0.2936457319 6.607029e-01
##  [724,] 0.362525595 0.3866939680 1.374912e-01
##  [725,] 0.318229499 0.0540389715 3.058810e-03
##  [726,] 0.318229499 0.0540389715 3.058810e-03
##  [727,] 0.440355309 0.2596967205 5.105149e-02
##  [728,] 0.090631399 0.0030210466 3.356718e-05
##  [729,] 0.266544426 0.0339238361 1.439193e-03
##  [730,] 0.440355309 0.2596967205 5.105149e-02
##  [731,] 0.321175019 0.4163379880 1.798991e-01
##  [732,] 0.416337988 0.3211750193 8.258786e-02
##  [733,] 0.406028666 0.1184250277 1.151354e-02
##  [734,] 0.397531973 0.3493462791 1.023338e-01
##  [735,] 0.293645732 0.0435030714 2.148300e-03
##  [736,] 0.406028666 0.1184250277 1.151354e-02
##  [737,] 0.407438488 0.3355375785 9.210835e-02
##  [738,] 0.397531973 0.3493462791 1.023338e-01
##  [739,] 0.291090430 0.4308138364 2.125348e-01
##  [740,] 0.375000000 0.3750000000 1.250000e-01
##  [741,] 0.266544426 0.0339238361 1.439193e-03
##  [742,] 0.211473264 0.4440938538 3.108657e-01
##  [743,] 0.179450170 0.4386559699 3.574234e-01
##  [744,] 0.163702964 0.4333313752 3.823512e-01
##  [745,] 0.360146521 0.0776786613 5.584740e-03
##  [746,] 0.349346279 0.3975319727 1.507880e-01
##  [747,] 0.340371253 0.0654560102 4.195898e-03
##  [748,] 0.438655970 0.1794501695 2.447048e-02
##  [749,] 0.340371253 0.0654560102 4.195898e-03
##  [750,] 0.444093854 0.2114732637 3.356718e-02
##  [751,] 0.433331375 0.1637029640 2.061445e-02
##  [752,] 0.440355309 0.2596967205 5.105149e-02
##  [753,] 0.227598100 0.4443581954 2.891855e-01
##  [754,] 0.349346279 0.3975319727 1.507880e-01
##  [755,] 0.426168977 0.1482326877 1.718640e-02
##  [756,] 0.406028666 0.1184250277 1.151354e-02
##  [757,] 0.362525595 0.3866939680 1.374912e-01
##  [758,] 0.266544426 0.0339238361 1.439193e-03
##  [759,] 0.430813836 0.2910904300 6.556091e-02
##  [760,] 0.362525595 0.3866939680 1.374912e-01
##  [761,] 0.444358195 0.2275981001 3.885821e-02
##  [762,] 0.406028666 0.1184250277 1.151354e-02
##  [763,] 0.163702964 0.4333313752 3.823512e-01
##  [764,] 0.104238696 0.3928997013 4.936432e-01
##  [765,] 0.444358195 0.2275981001 3.885821e-02
##  [766,] 0.397531973 0.3493462791 1.023338e-01
##  [767,] 0.195398778 0.4422182874 3.336033e-01
##  [768,] 0.195398778 0.4422182874 3.336033e-01
##  [769,] 0.131453291 0.0066840657 1.132892e-04
##  [770,] 0.397531973 0.3493462791 1.023338e-01
##  [771,] 0.438655970 0.1794501695 2.447048e-02
##  [772,] 0.438655970 0.1794501695 2.447048e-02
##  [773,] 0.436239133 0.2755194522 5.800410e-02
##  [774,] 0.306334128 0.4241549461 1.957638e-01
##  [775,] 0.318229499 0.0540389715 3.058810e-03
##  [776,] 0.438655970 0.1794501695 2.447048e-02
##  [777,] 0.433331375 0.1637029640 2.061445e-02
##  [778,] 0.436239133 0.2755194522 5.800410e-02
##  [779,] 0.440355309 0.2596967205 5.105149e-02
##  [780,] 0.433331375 0.1637029640 2.061445e-02
##  [781,] 0.426168977 0.1482326877 1.718640e-02
##  [782,] 0.406028666 0.1184250277 1.151354e-02
##  [783,] 0.375000000 0.3750000000 1.250000e-01
##  [784,] 0.377630828 0.0906313987 7.250512e-03
##  [785,] 0.417093250 0.1331148669 1.416116e-02
##  [786,] 0.442218287 0.1953987782 2.877966e-02
##  [787,] 0.407438488 0.3355375785 9.210835e-02
##  [788,] 0.163702964 0.4333313752 3.823512e-01
##  [789,] 0.440355309 0.2596967205 5.105149e-02
##  [790,] 0.443086838 0.2436977611 4.467792e-02
##  [791,] 0.416337988 0.3211750193 8.258786e-02
##  [792,] 0.386693968 0.3625255950 1.132892e-01
##  [793,] 0.340371253 0.0654560102 4.195898e-03
##  [794,] 0.133114867 0.4170932496 4.356307e-01
##  [795,] 0.386693968 0.3625255950 1.132892e-01
##  [796,] 0.377630828 0.0906313987 7.250512e-03
##  [797,] 0.442218287 0.1953987782 2.877966e-02
##  [798,] 0.433331375 0.1637029640 2.061445e-02
##  [799,] 0.417093250 0.1331148669 1.416116e-02
##  [800,] 0.440355309 0.2596967205 5.105149e-02
##  [801,] 0.426168977 0.1482326877 1.718640e-02
##  [802,] 0.375000000 0.3750000000 1.250000e-01
##  [803,] 0.179450170 0.4386559699 3.574234e-01
##  [804,] 0.392899701 0.1042386963 9.218388e-03
##  [805,] 0.430813836 0.2910904300 6.556091e-02
##  [806,] 0.386693968 0.3625255950 1.132892e-01
##  [807,] 0.362525595 0.3866939680 1.374912e-01
##  [808,] 0.335537578 0.4074384881 1.649156e-01
##  [809,] 0.407438488 0.3355375785 9.210835e-02
##  [810,] 0.443086838 0.2436977611 4.467792e-02
##  [811,] 0.430813836 0.2910904300 6.556091e-02
##  [812,] 0.306334128 0.4241549461 1.957638e-01
##  [813,] 0.406028666 0.1184250277 1.151354e-02
##  [814,] 0.340371253 0.0654560102 4.195898e-03
##  [815,] 0.417093250 0.1331148669 1.416116e-02
##  [816,] 0.440355309 0.2596967205 5.105149e-02
##  [817,] 0.392899701 0.1042386963 9.218388e-03
##  [818,] 0.386693968 0.3625255950 1.132892e-01
##  [819,] 0.362525595 0.3866939680 1.374912e-01
##  [820,] 0.397531973 0.3493462791 1.023338e-01
##  [821,] 0.443086838 0.2436977611 4.467792e-02
##  [822,] 0.306334128 0.4241549461 1.957638e-01
##  [823,] 0.236850055 0.0253767916 9.063140e-04
##  [824,] 0.426168977 0.1482326877 1.718640e-02
##  [825,] 0.377630828 0.0906313987 7.250512e-03
##  [826,] 0.433331375 0.1637029640 2.061445e-02
##  [827,] 0.054038972 0.3182294988 6.246727e-01
##  [828,] 0.444358195 0.2275981001 3.885821e-02
##  [829,] 0.417093250 0.1331148669 1.416116e-02
##  [830,] 0.011681380 0.1693800141 8.186701e-01
##  [831,] 0.426168977 0.1482326877 1.718640e-02
##  [832,] 0.293645732 0.0435030714 2.148300e-03
##  [833,] 0.349346279 0.3975319727 1.507880e-01
##  [834,] 0.266544426 0.0339238361 1.439193e-03
##  [835,] 0.179450170 0.4386559699 3.574234e-01
##  [836,] 0.442218287 0.1953987782 2.877966e-02
##  [837,] 0.406028666 0.1184250277 1.151354e-02
##  [838,] 0.438655970 0.1794501695 2.447048e-02
##  [839,] 0.444358195 0.2275981001 3.885821e-02
##  [840,] 0.407438488 0.3355375785 9.210835e-02
##  [841,] 0.386693968 0.3625255950 1.132892e-01
##  [842,] 0.362525595 0.3866939680 1.374912e-01
##  [843,] 0.386693968 0.3625255950 1.132892e-01
##  [844,] 0.397531973 0.3493462791 1.023338e-01
##  [845,] 0.090631399 0.0030210466 3.356718e-05
##  [846,] 0.211473264 0.4440938538 3.108657e-01
##  [847,] 0.442218287 0.1953987782 2.877966e-02
##  [848,] 0.306334128 0.4241549461 1.957638e-01
##  [849,] 0.349346279 0.3975319727 1.507880e-01
##  [850,] 0.433331375 0.1637029640 2.061445e-02
##  [851,] 0.444093854 0.2114732637 3.356718e-02
##  [852,] 0.179450170 0.4386559699 3.574234e-01
##  [853,] 0.397531973 0.3493462791 1.023338e-01
##  [854,] 0.340371253 0.0654560102 4.195898e-03
##  [855,] 0.195398778 0.4422182874 3.336033e-01
##  [856,] 0.293645732 0.0435030714 2.148300e-03
##  [857,] 0.340371253 0.0654560102 4.195898e-03
##  [858,] 0.436239133 0.2755194522 5.800410e-02
##  [859,] 0.362525595 0.3866939680 1.374912e-01
##  [860,] 0.407438488 0.3355375785 9.210835e-02
##  [861,] 0.443086838 0.2436977611 4.467792e-02
##  [862,] 0.444093854 0.2114732637 3.356718e-02
##  [863,] 0.430813836 0.2910904300 6.556091e-02
##  [864,] 0.430813836 0.2910904300 6.556091e-02
##  [865,] 0.243697761 0.4430868383 2.685375e-01
##  [866,] 0.211473264 0.4440938538 3.108657e-01
##  [867,] 0.416337988 0.3211750193 8.258786e-02
##  [868,] 0.397531973 0.3493462791 1.023338e-01
##  [869,] 0.227598100 0.4443581954 2.891855e-01
##  [870,] 0.438655970 0.1794501695 2.447048e-02
##  [871,] 0.443086838 0.2436977611 4.467792e-02
##  [872,] 0.436239133 0.2755194522 5.800410e-02
##  [873,] 0.444093854 0.2114732637 3.356718e-02
##  [874,] 0.243697761 0.4430868383 2.685375e-01
##  [875,] 0.433331375 0.1637029640 2.061445e-02
##  [876,] 0.377630828 0.0906313987 7.250512e-03
##  [877,] 0.443086838 0.2436977611 4.467792e-02
##  [878,] 0.426168977 0.1482326877 1.718640e-02
##  [879,] 0.306334128 0.4241549461 1.957638e-01
##  [880,] 0.362525595 0.3866939680 1.374912e-01
##  [881,] 0.436239133 0.2755194522 5.800410e-02
##  [882,] 0.416337988 0.3211750193 8.258786e-02
##  [883,] 0.227598100 0.4443581954 2.891855e-01
##  [884,] 0.424154946 0.3063341278 7.374710e-02
##  [885,] 0.293645732 0.0435030714 2.148300e-03
##  [886,] 0.443086838 0.2436977611 4.467792e-02
##  [887,] 0.169380014 0.0116813803 2.685375e-04
##  [888,] 0.430813836 0.2910904300 6.556091e-02
##  [889,] 0.424154946 0.3063341278 7.374710e-02
##  [890,] 0.321175019 0.4163379880 1.798991e-01
##  [891,] 0.306334128 0.4241549461 1.957638e-01
##  [892,] 0.291090430 0.4308138364 2.125348e-01
##  [893,] 0.386693968 0.3625255950 1.132892e-01
##  [894,] 0.444093854 0.2114732637 3.356718e-02
##  [895,] 0.266544426 0.0339238361 1.439193e-03
##  [896,] 0.227598100 0.4443581954 2.891855e-01
##  [897,] 0.444093854 0.2114732637 3.356718e-02
##  [898,] 0.443086838 0.2436977611 4.467792e-02
##  [899,] 0.211473264 0.4440938538 3.108657e-01
##  [900,] 0.426168977 0.1482326877 1.718640e-02
##  [901,] 0.444358195 0.2275981001 3.885821e-02
##  [902,] 0.293645732 0.0435030714 2.148300e-03
##  [903,] 0.340371253 0.0654560102 4.195898e-03
##  [904,] 0.318229499 0.0540389715 3.058810e-03
##  [905,] 0.426168977 0.1482326877 1.718640e-02
##  [906,] 0.444093854 0.2114732637 3.356718e-02
##  [907,] 0.243697761 0.4430868383 2.685375e-01
##  [908,] 0.436239133 0.2755194522 5.800410e-02
##  [909,] 0.406028666 0.1184250277 1.151354e-02
##  [910,] 0.318229499 0.0540389715 3.058810e-03
##  [911,] 0.362525595 0.3866939680 1.374912e-01
##  [912,] 0.266544426 0.0339238361 1.439193e-03
##  [913,] 0.211473264 0.4440938538 3.108657e-01
##  [914,] 0.179450170 0.4386559699 3.574234e-01
##  [915,] 0.444358195 0.2275981001 3.885821e-02
##  [916,] 0.204487093 0.0179374643 5.244873e-04
##  [917,] 0.397531973 0.3493462791 1.023338e-01
##  [918,] 0.406028666 0.1184250277 1.151354e-02
##  [919,] 0.259696720 0.4403553087 2.488965e-01
##  [920,] 0.443086838 0.2436977611 4.467792e-02
##  [921,] 0.259696720 0.4403553087 2.488965e-01
##  [922,] 0.340371253 0.0654560102 4.195898e-03
##  [923,] 0.243697761 0.4430868383 2.685375e-01
##  [924,] 0.440355309 0.2596967205 5.105149e-02
##  [925,] 0.321175019 0.4163379880 1.798991e-01
##  [926,] 0.318229499 0.0540389715 3.058810e-03
##  [927,] 0.046838810 0.0007678494 4.195898e-06
##  [928,] 0.204487093 0.0179374643 5.244873e-04
##  [929,] 0.392899701 0.1042386963 9.218388e-03
##  [930,] 0.436239133 0.2755194522 5.800410e-02
##  [931,] 0.335537578 0.4074384881 1.649156e-01
##  [932,] 0.090631399 0.0030210466 3.356718e-05
##  [933,] 0.293645732 0.0435030714 2.148300e-03
##  [934,] 0.443086838 0.2436977611 4.467792e-02
##  [935,] 0.360146521 0.0776786613 5.584740e-03
##  [936,] 0.442218287 0.1953987782 2.877966e-02
##  [937,] 0.442218287 0.1953987782 2.877966e-02
##  [938,] 0.169380014 0.0116813803 2.685375e-04
##  [939,] 0.436239133 0.2755194522 5.800410e-02
##  [940,] 0.424154946 0.3063341278 7.374710e-02
##  [941,] 0.416337988 0.3211750193 8.258786e-02
##  [942,] 0.436239133 0.2755194522 5.800410e-02
##  [943,] 0.335537578 0.4074384881 1.649156e-01
##  [944,] 0.407438488 0.3355375785 9.210835e-02
##  [945,] 0.227598100 0.4443581954 2.891855e-01
##  [946,] 0.335537578 0.4074384881 1.649156e-01
##  [947,] 0.148232688 0.4261689772 4.084119e-01
##  [948,] 0.416337988 0.3211750193 8.258786e-02
##  [949,] 0.321175019 0.4163379880 1.798991e-01
##  [950,] 0.340371253 0.0654560102 4.195898e-03
##  [951,] 0.335537578 0.4074384881 1.649156e-01
##  [952,] 0.440355309 0.2596967205 5.105149e-02
##  [953,] 0.424154946 0.3063341278 7.374710e-02
##  [954,] 0.386693968 0.3625255950 1.132892e-01
##  [955,] 0.397531973 0.3493462791 1.023338e-01
##  [956,] 0.392899701 0.1042386963 9.218388e-03
##  [957,] 0.340371253 0.0654560102 4.195898e-03
##  [958,] 0.416337988 0.3211750193 8.258786e-02
##  [959,] 0.275519452 0.4362391326 2.302373e-01
##  [960,] 0.397531973 0.3493462791 1.023338e-01
##  [961,] 0.440355309 0.2596967205 5.105149e-02
##  [962,] 0.340371253 0.0654560102 4.195898e-03
##  [963,] 0.386693968 0.3625255950 1.132892e-01
##  [964,] 0.397531973 0.3493462791 1.023338e-01
##  [965,] 0.259696720 0.4403553087 2.488965e-01
##  [966,] 0.444358195 0.2275981001 3.885821e-02
##  [967,] 0.416337988 0.3211750193 8.258786e-02
##  [968,] 0.335537578 0.4074384881 1.649156e-01
##  [969,] 0.443086838 0.2436977611 4.467792e-02
##  [970,] 0.386693968 0.3625255950 1.132892e-01
##  [971,] 0.416337988 0.3211750193 8.258786e-02
##  [972,] 0.259696720 0.4403553087 2.488965e-01
##  [973,] 0.006684066 0.1314532913 8.617494e-01
##  [974,] 0.386693968 0.3625255950 1.132892e-01
##  [975,] 0.275519452 0.4362391326 2.302373e-01
##  [976,] 0.444358195 0.2275981001 3.885821e-02
##  [977,] 0.375000000 0.3750000000 1.250000e-01
##  [978,] 0.243697761 0.4430868383 2.685375e-01
##  [979,] 0.407438488 0.3355375785 9.210835e-02
##  [980,] 0.444358195 0.2275981001 3.885821e-02
##  [981,] 0.293645732 0.0435030714 2.148300e-03
##  [982,] 0.397531973 0.3493462791 1.023338e-01
##  [983,] 0.443086838 0.2436977611 4.467792e-02
##  [984,] 0.195398778 0.4422182874 3.336033e-01
##  [985,] 0.444093854 0.2114732637 3.356718e-02
##  [986,] 0.000000000 0.0000000000 0.000000e+00
##  [987,] 0.318229499 0.0540389715 3.058810e-03
##  [988,] 0.360146521 0.0776786613 5.584740e-03
##  [989,] 0.362525595 0.3866939680 1.374912e-01
##  [990,] 0.266544426 0.0339238361 1.439193e-03
##  [991,] 0.433331375 0.1637029640 2.061445e-02
##  [992,] 0.440355309 0.2596967205 5.105149e-02
##  [993,] 0.444093854 0.2114732637 3.356718e-02
##  [994,] 0.375000000 0.3750000000 1.250000e-01
##  [995,] 0.438655970 0.1794501695 2.447048e-02
##  [996,] 0.118425028 0.4060286664 4.640328e-01
##  [997,] 0.340371253 0.0654560102 4.195898e-03
##  [998,] 0.436239133 0.2755194522 5.800410e-02
##  [999,] 0.090631399 0.0030210466 3.356718e-05
## [1000,] 0.442218287 0.1953987782 2.877966e-02
## [1001,] 0.243697761 0.4430868383 2.685375e-01
## [1002,] 0.416337988 0.3211750193 8.258786e-02
## [1003,] 0.148232688 0.4261689772 4.084119e-01
## [1004,] 0.416337988 0.3211750193 8.258786e-02
## [1005,] 0.335537578 0.4074384881 1.649156e-01
## [1006,] 0.436239133 0.2755194522 5.800410e-02
## [1007,] 0.443086838 0.2436977611 4.467792e-02
## [1008,] 0.407438488 0.3355375785 9.210835e-02
## [1009,] 0.291090430 0.4308138364 2.125348e-01
## [1010,] 0.321175019 0.4163379880 1.798991e-01
## [1011,] 0.416337988 0.3211750193 8.258786e-02
## [1012,] 0.406028666 0.1184250277 1.151354e-02
## [1013,] 0.436239133 0.2755194522 5.800410e-02
## [1014,] 0.433331375 0.1637029640 2.061445e-02
## [1015,] 0.444093854 0.2114732637 3.356718e-02
## [1016,] 0.392899701 0.1042386963 9.218388e-03
## [1017,] 0.440355309 0.2596967205 5.105149e-02
## [1018,] 0.416337988 0.3211750193 8.258786e-02
## [1019,] 0.362525595 0.3866939680 1.374912e-01
## [1020,] 0.360146521 0.0776786613 5.584740e-03
## [1021,] 0.406028666 0.1184250277 1.151354e-02
## [1022,] 0.349346279 0.3975319727 1.507880e-01
## [1023,] 0.360146521 0.0776786613 5.584740e-03
## [1024,] 0.406028666 0.1184250277 1.151354e-02
## [1025,] 0.392899701 0.1042386963 9.218388e-03
## [1026,] 0.360146521 0.0776786613 5.584740e-03
## [1027,] 0.340371253 0.0654560102 4.195898e-03
## [1028,] 0.362525595 0.3866939680 1.374912e-01
## [1029,] 0.375000000 0.3750000000 1.250000e-01
## [1030,] 0.293645732 0.0435030714 2.148300e-03
## [1031,] 0.392899701 0.1042386963 9.218388e-03
## [1032,] 0.179450170 0.4386559699 3.574234e-01
## [1033,] 0.433331375 0.1637029640 2.061445e-02
## [1034,] 0.291090430 0.4308138364 2.125348e-01
## [1035,] 0.430813836 0.2910904300 6.556091e-02
## [1036,] 0.243697761 0.4430868383 2.685375e-01
## [1037,] 0.444093854 0.2114732637 3.356718e-02
## [1038,] 0.375000000 0.3750000000 1.250000e-01
## [1039,] 0.179450170 0.4386559699 3.574234e-01
## [1040,] 0.293645732 0.0435030714 2.148300e-03
## [1041,] 0.407438488 0.3355375785 9.210835e-02
## [1042,] 0.243697761 0.4430868383 2.685375e-01
## [1043,] 0.163702964 0.4333313752 3.823512e-01
## [1044,] 0.104238696 0.3928997013 4.936432e-01
## [1045,] 0.349346279 0.3975319727 1.507880e-01
## [1046,] 0.407438488 0.3355375785 9.210835e-02
## [1047,] 0.443086838 0.2436977611 4.467792e-02
## [1048,] 0.131453291 0.0066840657 1.132892e-04
## [1049,] 0.349346279 0.3975319727 1.507880e-01
## [1050,] 0.430813836 0.2910904300 6.556091e-02
## [1051,] 0.416337988 0.3211750193 8.258786e-02
## [1052,] 0.417093250 0.1331148669 1.416116e-02
## [1053,] 0.444093854 0.2114732637 3.356718e-02
## [1054,] 0.424154946 0.3063341278 7.374710e-02
## [1055,] 0.362525595 0.3866939680 1.374912e-01
## [1056,] 0.291090430 0.4308138364 2.125348e-01
## [1057,] 0.375000000 0.3750000000 1.250000e-01
## [1058,] 0.443086838 0.2436977611 4.467792e-02
## [1059,] 0.131453291 0.0066840657 1.132892e-04
## [1060,] 0.211473264 0.4440938538 3.108657e-01
## [1061,] 0.195398778 0.4422182874 3.336033e-01
## [1062,] 0.424154946 0.3063341278 7.374710e-02
## [1063,] 0.430813836 0.2910904300 6.556091e-02
## [1064,] 0.360146521 0.0776786613 5.584740e-03
## [1065,] 0.293645732 0.0435030714 2.148300e-03
## [1066,] 0.340371253 0.0654560102 4.195898e-03
## [1067,] 0.444093854 0.2114732637 3.356718e-02
## [1068,] 0.416337988 0.3211750193 8.258786e-02
## [1069,] 0.444358195 0.2275981001 3.885821e-02
## [1070,] 0.424154946 0.3063341278 7.374710e-02
## [1071,] 0.416337988 0.3211750193 8.258786e-02
## [1072,] 0.275519452 0.4362391326 2.302373e-01
## [1073,] 0.443086838 0.2436977611 4.467792e-02
## [1074,] 0.054038972 0.3182294988 6.246727e-01
## [1075,] 0.377630828 0.0906313987 7.250512e-03
## [1076,] 0.416337988 0.3211750193 8.258786e-02
## [1077,] 0.440355309 0.2596967205 5.105149e-02
## [1078,] 0.443086838 0.2436977611 4.467792e-02
## [1079,] 0.407438488 0.3355375785 9.210835e-02
## [1080,] 0.444093854 0.2114732637 3.356718e-02
## [1081,] 0.293645732 0.0435030714 2.148300e-03
## [1082,] 0.407438488 0.3355375785 9.210835e-02
## [1083,] 0.436239133 0.2755194522 5.800410e-02
## [1084,] 0.426168977 0.1482326877 1.718640e-02
## [1085,] 0.407438488 0.3355375785 9.210835e-02
## [1086,] 0.442218287 0.1953987782 2.877966e-02
## [1087,] 0.335537578 0.4074384881 1.649156e-01
## [1088,] 0.430813836 0.2910904300 6.556091e-02
## [1089,] 0.335537578 0.4074384881 1.649156e-01
## [1090,] 0.397531973 0.3493462791 1.023338e-01
## [1091,] 0.444093854 0.2114732637 3.356718e-02
## [1092,] 0.321175019 0.4163379880 1.798991e-01
## [1093,] 0.433331375 0.1637029640 2.061445e-02
## [1094,] 0.444358195 0.2275981001 3.885821e-02
## [1095,] 0.416337988 0.3211750193 8.258786e-02
## [1096,] 0.195398778 0.4422182874 3.336033e-01
## [1097,] 0.148232688 0.4261689772 4.084119e-01
## [1098,] 0.444358195 0.2275981001 3.885821e-02
## [1099,] 0.407438488 0.3355375785 9.210835e-02
## [1100,] 0.266544426 0.0339238361 1.439193e-03
## [1101,] 0.243697761 0.4430868383 2.685375e-01
## [1102,] 0.335537578 0.4074384881 1.649156e-01
## [1103,] 0.416337988 0.3211750193 8.258786e-02
## [1104,] 0.440355309 0.2596967205 5.105149e-02
## [1105,] 0.436239133 0.2755194522 5.800410e-02
## [1106,] 0.392899701 0.1042386963 9.218388e-03
## [1107,] 0.397531973 0.3493462791 1.023338e-01
## [1108,] 0.444358195 0.2275981001 3.885821e-02
## [1109,] 0.321175019 0.4163379880 1.798991e-01
## [1110,] 0.440355309 0.2596967205 5.105149e-02
## [1111,] 0.163702964 0.4333313752 3.823512e-01
## [1112,] 0.204487093 0.0179374643 5.244873e-04
## [1113,] 0.179450170 0.4386559699 3.574234e-01
## [1114,] 0.430813836 0.2910904300 6.556091e-02
## [1115,] 0.360146521 0.0776786613 5.584740e-03
## [1116,] 0.426168977 0.1482326877 1.718640e-02
## [1117,] 0.444093854 0.2114732637 3.356718e-02
## [1118,] 0.266544426 0.0339238361 1.439193e-03
## [1119,] 0.375000000 0.3750000000 1.250000e-01
## [1120,] 0.407438488 0.3355375785 9.210835e-02
## [1121,] 0.377630828 0.0906313987 7.250512e-03
## [1122,] 0.417093250 0.1331148669 1.416116e-02
## [1123,] 0.360146521 0.0776786613 5.584740e-03
## [1124,] 0.406028666 0.1184250277 1.151354e-02
## [1125,] 0.306334128 0.4241549461 1.957638e-01
## [1126,] 0.443086838 0.2436977611 4.467792e-02
## [1127,] 0.377630828 0.0906313987 7.250512e-03
## [1128,] 0.375000000 0.3750000000 1.250000e-01
## [1129,] 0.266544426 0.0339238361 1.439193e-03
## [1130,] 0.424154946 0.3063341278 7.374710e-02
## [1131,] 0.440355309 0.2596967205 5.105149e-02
## [1132,] 0.306334128 0.4241549461 1.957638e-01
## [1133,] 0.266544426 0.0339238361 1.439193e-03
## [1134,] 0.163702964 0.4333313752 3.823512e-01
## [1135,] 0.375000000 0.3750000000 1.250000e-01
## [1136,] 0.236850055 0.0253767916 9.063140e-04
## [1137,] 0.259696720 0.4403553087 2.488965e-01
## [1138,] 0.397531973 0.3493462791 1.023338e-01
## [1139,] 0.424154946 0.3063341278 7.374710e-02
## [1140,] 0.275519452 0.4362391326 2.302373e-01
## [1141,] 0.426168977 0.1482326877 1.718640e-02
## [1142,] 0.204487093 0.0179374643 5.244873e-04
## [1143,] 0.377630828 0.0906313987 7.250512e-03
## [1144,] 0.444093854 0.2114732637 3.356718e-02
## [1145,] 0.243697761 0.4430868383 2.685375e-01
## [1146,] 0.438655970 0.1794501695 2.447048e-02
## [1147,] 0.386693968 0.3625255950 1.132892e-01
## [1148,] 0.433331375 0.1637029640 2.061445e-02
## [1149,] 0.169380014 0.0116813803 2.685375e-04
## [1150,] 0.362525595 0.3866939680 1.374912e-01
## [1151,] 0.243697761 0.4430868383 2.685375e-01
## [1152,] 0.090631399 0.0030210466 3.356718e-05
## [1153,] 0.444358195 0.2275981001 3.885821e-02
## [1154,] 0.406028666 0.1184250277 1.151354e-02
## [1155,] 0.236850055 0.0253767916 9.063140e-04
## [1156,] 0.321175019 0.4163379880 1.798991e-01
## [1157,] 0.433331375 0.1637029640 2.061445e-02
## [1158,] 0.236850055 0.0253767916 9.063140e-04
## [1159,] 0.259696720 0.4403553087 2.488965e-01
## [1160,] 0.430813836 0.2910904300 6.556091e-02
## [1161,] 0.417093250 0.1331148669 1.416116e-02
## [1162,] 0.443086838 0.2436977611 4.467792e-02
## [1163,] 0.444358195 0.2275981001 3.885821e-02
## [1164,] 0.433331375 0.1637029640 2.061445e-02
## [1165,] 0.433331375 0.1637029640 2.061445e-02
## [1166,] 0.259696720 0.4403553087 2.488965e-01
## [1167,] 0.386693968 0.3625255950 1.132892e-01
## [1168,] 0.440355309 0.2596967205 5.105149e-02
## [1169,] 0.227598100 0.4443581954 2.891855e-01
## [1170,] 0.291090430 0.4308138364 2.125348e-01
## [1171,] 0.306334128 0.4241549461 1.957638e-01
## [1172,] 0.426168977 0.1482326877 1.718640e-02
## [1173,] 0.430813836 0.2910904300 6.556091e-02
## [1174,] 0.430813836 0.2910904300 6.556091e-02
## [1175,] 0.179450170 0.4386559699 3.574234e-01
## [1176,] 0.416337988 0.3211750193 8.258786e-02
## [1177,] 0.443086838 0.2436977611 4.467792e-02
## [1178,] 0.417093250 0.1331148669 1.416116e-02
## [1179,] 0.416337988 0.3211750193 8.258786e-02
## [1180,] 0.131453291 0.0066840657 1.132892e-04
## [1181,] 0.306334128 0.4241549461 1.957638e-01
## [1182,] 0.430813836 0.2910904300 6.556091e-02
## [1183,] 0.306334128 0.4241549461 1.957638e-01
## [1184,] 0.433331375 0.1637029640 2.061445e-02
## [1185,] 0.430813836 0.2910904300 6.556091e-02
## [1186,] 0.133114867 0.4170932496 4.356307e-01
## [1187,] 0.236850055 0.0253767916 9.063140e-04
## [1188,] 0.416337988 0.3211750193 8.258786e-02
## [1189,] 0.438655970 0.1794501695 2.447048e-02
## [1190,] 0.416337988 0.3211750193 8.258786e-02
## [1191,] 0.417093250 0.1331148669 1.416116e-02
## [1192,] 0.442218287 0.1953987782 2.877966e-02
## [1193,] 0.204487093 0.0179374643 5.244873e-04
## [1194,] 0.195398778 0.4422182874 3.336033e-01
## [1195,] 0.397531973 0.3493462791 1.023338e-01
## [1196,] 0.360146521 0.0776786613 5.584740e-03
## [1197,] 0.442218287 0.1953987782 2.877966e-02
## [1198,] 0.259696720 0.4403553087 2.488965e-01
## [1199,] 0.444358195 0.2275981001 3.885821e-02
## [1200,] 0.227598100 0.4443581954 2.891855e-01
## [1201,] 0.392899701 0.1042386963 9.218388e-03
## [1202,] 0.293645732 0.0435030714 2.148300e-03
## [1203,] 0.349346279 0.3975319727 1.507880e-01
## [1204,] 0.362525595 0.3866939680 1.374912e-01
## [1205,] 0.406028666 0.1184250277 1.151354e-02
## [1206,] 0.211473264 0.4440938538 3.108657e-01
## [1207,] 0.440355309 0.2596967205 5.105149e-02
## [1208,] 0.406028666 0.1184250277 1.151354e-02
## [1209,] 0.293645732 0.0435030714 2.148300e-03
## [1210,] 0.440355309 0.2596967205 5.105149e-02
## [1211,] 0.362525595 0.3866939680 1.374912e-01
## [1212,] 0.430813836 0.2910904300 6.556091e-02
## [1213,] 0.046838810 0.0007678494 4.195898e-06
## [1214,] 0.436239133 0.2755194522 5.800410e-02
## [1215,] 0.321175019 0.4163379880 1.798991e-01
## [1216,] 0.169380014 0.0116813803 2.685375e-04
## [1217,] 0.375000000 0.3750000000 1.250000e-01
## [1218,] 0.417093250 0.1331148669 1.416116e-02
## [1219,] 0.392899701 0.1042386963 9.218388e-03
## [1220,] 0.430813836 0.2910904300 6.556091e-02
## [1221,] 0.259696720 0.4403553087 2.488965e-01
## [1222,] 0.386693968 0.3625255950 1.132892e-01
## [1223,] 0.243697761 0.4430868383 2.685375e-01
## [1224,] 0.362525595 0.3866939680 1.374912e-01
## [1225,] 0.335537578 0.4074384881 1.649156e-01
## [1226,] 0.386693968 0.3625255950 1.132892e-01
## [1227,] 0.321175019 0.4163379880 1.798991e-01
## [1228,] 0.430813836 0.2910904300 6.556091e-02
## [1229,] 0.266544426 0.0339238361 1.439193e-03
## [1230,] 0.433331375 0.1637029640 2.061445e-02
## [1231,] 0.438655970 0.1794501695 2.447048e-02
## [1232,] 0.430813836 0.2910904300 6.556091e-02
## [1233,] 0.440355309 0.2596967205 5.105149e-02
## [1234,] 0.335537578 0.4074384881 1.649156e-01
## [1235,] 0.386693968 0.3625255950 1.132892e-01
## [1236,] 0.349346279 0.3975319727 1.507880e-01
## [1237,] 0.442218287 0.1953987782 2.877966e-02
## [1238,] 0.386693968 0.3625255950 1.132892e-01
## [1239,] 0.436239133 0.2755194522 5.800410e-02
## [1240,] 0.430813836 0.2910904300 6.556091e-02
## [1241,] 0.444093854 0.2114732637 3.356718e-02
## [1242,] 0.204487093 0.0179374643 5.244873e-04
## [1243,] 0.306334128 0.4241549461 1.957638e-01
## [1244,] 0.118425028 0.4060286664 4.640328e-01
## [1245,] 0.397531973 0.3493462791 1.023338e-01
## [1246,] 0.433331375 0.1637029640 2.061445e-02
## [1247,] 0.433331375 0.1637029640 2.061445e-02
## [1248,] 0.443086838 0.2436977611 4.467792e-02
## [1249,] 0.440355309 0.2596967205 5.105149e-02
## [1250,] 0.443086838 0.2436977611 4.467792e-02
## [1251,] 0.362525595 0.3866939680 1.374912e-01
## [1252,] 0.433331375 0.1637029640 2.061445e-02
## [1253,] 0.430813836 0.2910904300 6.556091e-02
## [1254,] 0.293645732 0.0435030714 2.148300e-03
## [1255,] 0.195398778 0.4422182874 3.336033e-01
## [1256,] 0.362525595 0.3866939680 1.374912e-01
## [1257,] 0.169380014 0.0116813803 2.685375e-04
## [1258,] 0.179450170 0.4386559699 3.574234e-01
## [1259,] 0.291090430 0.4308138364 2.125348e-01
## [1260,] 0.360146521 0.0776786613 5.584740e-03
## [1261,] 0.444358195 0.2275981001 3.885821e-02
## [1262,] 0.054038972 0.3182294988 6.246727e-01
## [1263,] 0.169380014 0.0116813803 2.685375e-04
## [1264,] 0.386693968 0.3625255950 1.132892e-01
## [1265,] 0.433331375 0.1637029640 2.061445e-02
## [1266,] 0.407438488 0.3355375785 9.210835e-02
## [1267,] 0.291090430 0.4308138364 2.125348e-01
## [1268,] 0.438655970 0.1794501695 2.447048e-02
## [1269,] 0.259696720 0.4403553087 2.488965e-01
## [1270,] 0.211473264 0.4440938538 3.108657e-01
## [1271,] 0.440355309 0.2596967205 5.105149e-02
## [1272,] 0.275519452 0.4362391326 2.302373e-01
## [1273,] 0.406028666 0.1184250277 1.151354e-02
## [1274,] 0.438655970 0.1794501695 2.447048e-02
## [1275,] 0.340371253 0.0654560102 4.195898e-03
## [1276,] 0.211473264 0.4440938538 3.108657e-01
## [1277,] 0.440355309 0.2596967205 5.105149e-02
## [1278,] 0.291090430 0.4308138364 2.125348e-01
## [1279,] 0.407438488 0.3355375785 9.210835e-02
## [1280,] 0.179450170 0.4386559699 3.574234e-01
## [1281,] 0.424154946 0.3063341278 7.374710e-02
## [1282,] 0.438655970 0.1794501695 2.447048e-02
## [1283,] 0.440355309 0.2596967205 5.105149e-02
## [1284,] 0.169380014 0.0116813803 2.685375e-04
## [1285,] 0.349346279 0.3975319727 1.507880e-01
## [1286,] 0.259696720 0.4403553087 2.488965e-01
## [1287,] 0.291090430 0.4308138364 2.125348e-01
## [1288,] 0.438655970 0.1794501695 2.447048e-02
## [1289,] 0.406028666 0.1184250277 1.151354e-02
## [1290,] 0.438655970 0.1794501695 2.447048e-02
## [1291,] 0.340371253 0.0654560102 4.195898e-03
## [1292,] 0.444358195 0.2275981001 3.885821e-02
## [1293,] 0.436239133 0.2755194522 5.800410e-02
## [1294,] 0.291090430 0.4308138364 2.125348e-01
## [1295,] 0.444358195 0.2275981001 3.885821e-02
## [1296,] 0.436239133 0.2755194522 5.800410e-02
## [1297,] 0.417093250 0.1331148669 1.416116e-02
## [1298,] 0.204487093 0.0179374643 5.244873e-04
## [1299,] 0.259696720 0.4403553087 2.488965e-01
## [1300,] 0.318229499 0.0540389715 3.058810e-03
## [1301,] 0.266544426 0.0339238361 1.439193e-03
## [1302,] 0.318229499 0.0540389715 3.058810e-03
## [1303,] 0.417093250 0.1331148669 1.416116e-02
## [1304,] 0.169380014 0.0116813803 2.685375e-04
## [1305,] 0.397531973 0.3493462791 1.023338e-01
## [1306,] 0.397531973 0.3493462791 1.023338e-01
## [1307,] 0.392899701 0.1042386963 9.218388e-03
## [1308,] 0.407438488 0.3355375785 9.210835e-02
## [1309,] 0.397531973 0.3493462791 1.023338e-01
## [1310,] 0.443086838 0.2436977611 4.467792e-02
## [1311,] 0.349346279 0.3975319727 1.507880e-01
## [1312,] 0.392899701 0.1042386963 9.218388e-03
## [1313,] 0.243697761 0.4430868383 2.685375e-01
## [1314,] 0.386693968 0.3625255950 1.132892e-01
## [1315,] 0.306334128 0.4241549461 1.957638e-01
## [1316,] 0.275519452 0.4362391326 2.302373e-01
## [1317,] 0.195398778 0.4422182874 3.336033e-01
## [1318,] 0.406028666 0.1184250277 1.151354e-02
## [1319,] 0.211473264 0.4440938538 3.108657e-01
## [1320,] 0.436239133 0.2755194522 5.800410e-02
## [1321,] 0.321175019 0.4163379880 1.798991e-01
## [1322,] 0.406028666 0.1184250277 1.151354e-02
## [1323,] 0.362525595 0.3866939680 1.374912e-01
## [1324,] 0.443086838 0.2436977611 4.467792e-02
## [1325,] 0.436239133 0.2755194522 5.800410e-02
## [1326,] 0.433331375 0.1637029640 2.061445e-02
## [1327,] 0.417093250 0.1331148669 1.416116e-02
## [1328,] 0.417093250 0.1331148669 1.416116e-02
## [1329,] 0.444093854 0.2114732637 3.356718e-02
## [1330,] 0.436239133 0.2755194522 5.800410e-02
## [1331,] 0.243697761 0.4430868383 2.685375e-01
## [1332,] 0.416337988 0.3211750193 8.258786e-02
## [1333,] 0.377630828 0.0906313987 7.250512e-03
## [1334,] 0.426168977 0.1482326877 1.718640e-02
## [1335,] 0.430813836 0.2910904300 6.556091e-02
## [1336,] 0.424154946 0.3063341278 7.374710e-02
## [1337,] 0.340371253 0.0654560102 4.195898e-03
## [1338,] 0.407438488 0.3355375785 9.210835e-02
## [1339,] 0.438655970 0.1794501695 2.447048e-02
## [1340,] 0.442218287 0.1953987782 2.877966e-02
## [1341,] 0.397531973 0.3493462791 1.023338e-01
## [1342,] 0.444093854 0.2114732637 3.356718e-02
## [1343,] 0.440355309 0.2596967205 5.105149e-02
## [1344,] 0.179450170 0.4386559699 3.574234e-01
## [1345,] 0.443086838 0.2436977611 4.467792e-02
## [1346,] 0.424154946 0.3063341278 7.374710e-02
## [1347,] 0.275519452 0.4362391326 2.302373e-01
## [1348,] 0.349346279 0.3975319727 1.507880e-01
## [1349,] 0.335537578 0.4074384881 1.649156e-01
## [1350,] 0.318229499 0.0540389715 3.058810e-03
## [1351,] 0.335537578 0.4074384881 1.649156e-01
## [1352,] 0.349346279 0.3975319727 1.507880e-01
## [1353,] 0.340371253 0.0654560102 4.195898e-03
## [1354,] 0.375000000 0.3750000000 1.250000e-01
## [1355,] 0.195398778 0.4422182874 3.336033e-01
## [1356,] 0.204487093 0.0179374643 5.244873e-04
## [1357,] 0.321175019 0.4163379880 1.798991e-01
## [1358,] 0.291090430 0.4308138364 2.125348e-01
## [1359,] 0.386693968 0.3625255950 1.132892e-01
## [1360,] 0.362525595 0.3866939680 1.374912e-01
## [1361,] 0.392899701 0.1042386963 9.218388e-03
## [1362,] 0.321175019 0.4163379880 1.798991e-01
## [1363,] 0.430813836 0.2910904300 6.556091e-02
## [1364,] 0.090631399 0.0030210466 3.356718e-05
## [1365,] 0.407438488 0.3355375785 9.210835e-02
## [1366,] 0.275519452 0.4362391326 2.302373e-01
## [1367,] 0.424154946 0.3063341278 7.374710e-02
## [1368,] 0.204487093 0.0179374643 5.244873e-04
## [1369,] 0.436239133 0.2755194522 5.800410e-02
## [1370,] 0.406028666 0.1184250277 1.151354e-02
## [1371,] 0.430813836 0.2910904300 6.556091e-02
## [1372,] 0.259696720 0.4403553087 2.488965e-01
## [1373,] 0.104238696 0.3928997013 4.936432e-01
## [1374,] 0.375000000 0.3750000000 1.250000e-01
## [1375,] 0.360146521 0.0776786613 5.584740e-03
## [1376,] 0.433331375 0.1637029640 2.061445e-02
## [1377,] 0.444358195 0.2275981001 3.885821e-02
## [1378,] 0.417093250 0.1331148669 1.416116e-02
## [1379,] 0.321175019 0.4163379880 1.798991e-01
## [1380,] 0.430813836 0.2910904300 6.556091e-02
## [1381,] 0.438655970 0.1794501695 2.447048e-02
## [1382,] 0.444093854 0.2114732637 3.356718e-02
## [1383,] 0.243697761 0.4430868383 2.685375e-01
## [1384,] 0.416337988 0.3211750193 8.258786e-02
## [1385,] 0.426168977 0.1482326877 1.718640e-02
## [1386,] 0.377630828 0.0906313987 7.250512e-03
## [1387,] 0.131453291 0.0066840657 1.132892e-04
## [1388,] 0.236850055 0.0253767916 9.063140e-04
## [1389,] 0.386693968 0.3625255950 1.132892e-01
## [1390,] 0.392899701 0.1042386963 9.218388e-03
## [1391,] 0.424154946 0.3063341278 7.374710e-02
## [1392,] 0.377630828 0.0906313987 7.250512e-03
## [1393,] 0.406028666 0.1184250277 1.151354e-02
## [1394,] 0.444358195 0.2275981001 3.885821e-02
## [1395,] 0.436239133 0.2755194522 5.800410e-02
## [1396,] 0.236850055 0.0253767916 9.063140e-04
## [1397,] 0.424154946 0.3063341278 7.374710e-02
## [1398,] 0.377630828 0.0906313987 7.250512e-03
## [1399,] 0.243697761 0.4430868383 2.685375e-01
## [1400,] 0.275519452 0.4362391326 2.302373e-01
## [1401,] 0.340371253 0.0654560102 4.195898e-03
## [1402,] 0.169380014 0.0116813803 2.685375e-04
## [1403,] 0.442218287 0.1953987782 2.877966e-02
## [1404,] 0.000000000 0.0000000000 0.000000e+00
## [1405,] 0.430813836 0.2910904300 6.556091e-02
## [1406,] 0.438655970 0.1794501695 2.447048e-02
## [1407,] 0.397531973 0.3493462791 1.023338e-01
## [1408,] 0.335537578 0.4074384881 1.649156e-01
## [1409,] 0.426168977 0.1482326877 1.718640e-02
## [1410,] 0.179450170 0.4386559699 3.574234e-01
## [1411,] 0.386693968 0.3625255950 1.132892e-01
## [1412,] 0.433331375 0.1637029640 2.061445e-02
## [1413,] 0.436239133 0.2755194522 5.800410e-02
## [1414,] 0.426168977 0.1482326877 1.718640e-02
## [1415,] 0.362525595 0.3866939680 1.374912e-01
## [1416,] 0.362525595 0.3866939680 1.374912e-01
## [1417,] 0.275519452 0.4362391326 2.302373e-01
## [1418,] 0.362525595 0.3866939680 1.374912e-01
## [1419,] 0.424154946 0.3063341278 7.374710e-02
## [1420,] 0.377630828 0.0906313987 7.250512e-03
## [1421,] 0.426168977 0.1482326877 1.718640e-02
## [1422,] 0.362525595 0.3866939680 1.374912e-01
## [1423,] 0.349346279 0.3975319727 1.507880e-01
## [1424,] 0.443086838 0.2436977611 4.467792e-02
## [1425,] 0.426168977 0.1482326877 1.718640e-02
## [1426,] 0.438655970 0.1794501695 2.447048e-02
## [1427,] 0.424154946 0.3063341278 7.374710e-02
## [1428,] 0.438655970 0.1794501695 2.447048e-02
## [1429,] 0.179450170 0.4386559699 3.574234e-01
## [1430,] 0.417093250 0.1331148669 1.416116e-02
## [1431,] 0.424154946 0.3063341278 7.374710e-02
## [1432,] 0.000000000 0.0000000000 1.000000e+00
## [1433,] 0.416337988 0.3211750193 8.258786e-02
## [1434,] 0.243697761 0.4430868383 2.685375e-01
## [1435,] 0.349346279 0.3975319727 1.507880e-01
## [1436,] 0.340371253 0.0654560102 4.195898e-03
## [1437,] 0.442218287 0.1953987782 2.877966e-02
## [1438,] 0.275519452 0.4362391326 2.302373e-01
## [1439,] 0.275519452 0.4362391326 2.302373e-01
## [1440,] 0.426168977 0.1482326877 1.718640e-02
## [1441,] 0.438655970 0.1794501695 2.447048e-02
## [1442,] 0.416337988 0.3211750193 8.258786e-02
## [1443,] 0.438655970 0.1794501695 2.447048e-02
## [1444,] 0.204487093 0.0179374643 5.244873e-04
## [1445,] 0.417093250 0.1331148669 1.416116e-02
## [1446,] 0.386693968 0.3625255950 1.132892e-01
## [1447,] 0.340371253 0.0654560102 4.195898e-03
## [1448,] 0.442218287 0.1953987782 2.877966e-02
## [1449,] 0.169380014 0.0116813803 2.685375e-04
## [1450,] 0.211473264 0.4440938538 3.108657e-01
## [1451,] 0.377630828 0.0906313987 7.250512e-03
## [1452,] 0.362525595 0.3866939680 1.374912e-01
## [1453,] 0.291090430 0.4308138364 2.125348e-01
## [1454,] 0.293645732 0.0435030714 2.148300e-03
## [1455,] 0.436239133 0.2755194522 5.800410e-02
## [1456,] 0.054038972 0.3182294988 6.246727e-01
## [1457,] 0.417093250 0.1331148669 1.416116e-02
## [1458,] 0.375000000 0.3750000000 1.250000e-01
## [1459,] 0.416337988 0.3211750193 8.258786e-02
## [1460,] 0.440355309 0.2596967205 5.105149e-02
## [1461,] 0.227598100 0.4443581954 2.891855e-01
## [1462,] 0.417093250 0.1331148669 1.416116e-02
## [1463,] 0.204487093 0.0179374643 5.244873e-04
## [1464,] 0.406028666 0.1184250277 1.151354e-02
## [1465,] 0.377630828 0.0906313987 7.250512e-03
## [1466,] 0.306334128 0.4241549461 1.957638e-01
## [1467,] 0.362525595 0.3866939680 1.374912e-01
## [1468,] 0.259696720 0.4403553087 2.488965e-01
## [1469,] 0.377630828 0.0906313987 7.250512e-03
## [1470,] 0.406028666 0.1184250277 1.151354e-02
## [1471,] 0.386693968 0.3625255950 1.132892e-01
## [1472,] 0.392899701 0.1042386963 9.218388e-03
## [1473,] 0.362525595 0.3866939680 1.374912e-01
## [1474,] 0.397531973 0.3493462791 1.023338e-01
## [1475,] 0.442218287 0.1953987782 2.877966e-02
## [1476,] 0.236850055 0.0253767916 9.063140e-04
## [1477,] 0.321175019 0.4163379880 1.798991e-01
## [1478,] 0.444358195 0.2275981001 3.885821e-02
## [1479,] 0.397531973 0.3493462791 1.023338e-01
## [1480,] 0.438655970 0.1794501695 2.447048e-02
## [1481,] 0.426168977 0.1482326877 1.718640e-02
## [1482,] 0.416337988 0.3211750193 8.258786e-02
## [1483,] 0.211473264 0.4440938538 3.108657e-01
## [1484,] 0.430813836 0.2910904300 6.556091e-02
## [1485,] 0.433331375 0.1637029640 2.061445e-02
## [1486,] 0.362525595 0.3866939680 1.374912e-01
## [1487,] 0.275519452 0.4362391326 2.302373e-01
## [1488,] 0.433331375 0.1637029640 2.061445e-02
## [1489,] 0.204487093 0.0179374643 5.244873e-04
## [1490,] 0.416337988 0.3211750193 8.258786e-02
## [1491,] 0.306334128 0.4241549461 1.957638e-01
## [1492,] 0.436239133 0.2755194522 5.800410e-02
## [1493,] 0.349346279 0.3975319727 1.507880e-01
## [1494,] 0.375000000 0.3750000000 1.250000e-01
## [1495,] 0.386693968 0.3625255950 1.132892e-01
## [1496,] 0.362525595 0.3866939680 1.374912e-01
## [1497,] 0.442218287 0.1953987782 2.877966e-02
## [1498,] 0.444093854 0.2114732637 3.356718e-02
## [1499,] 0.243697761 0.4430868383 2.685375e-01
## [1500,] 0.349346279 0.3975319727 1.507880e-01
## [1501,] 0.349346279 0.3975319727 1.507880e-01
## [1502,] 0.424154946 0.3063341278 7.374710e-02
## [1503,] 0.430813836 0.2910904300 6.556091e-02
## [1504,] 0.227598100 0.4443581954 2.891855e-01
## [1505,] 0.195398778 0.4422182874 3.336033e-01
## [1506,] 0.443086838 0.2436977611 4.467792e-02
## [1507,] 0.291090430 0.4308138364 2.125348e-01
## [1508,] 0.440355309 0.2596967205 5.105149e-02
## [1509,] 0.118425028 0.4060286664 4.640328e-01
## [1510,] 0.195398778 0.4422182874 3.336033e-01
## [1511,] 0.426168977 0.1482326877 1.718640e-02
## [1512,] 0.440355309 0.2596967205 5.105149e-02
## [1513,] 0.386693968 0.3625255950 1.132892e-01
## [1514,] 0.306334128 0.4241549461 1.957638e-01
## [1515,] 0.424154946 0.3063341278 7.374710e-02
## [1516,] 0.259696720 0.4403553087 2.488965e-01
## [1517,] 0.321175019 0.4163379880 1.798991e-01
## [1518,] 0.179450170 0.4386559699 3.574234e-01
## [1519,] 0.443086838 0.2436977611 4.467792e-02
## [1520,] 0.444358195 0.2275981001 3.885821e-02
## [1521,] 0.416337988 0.3211750193 8.258786e-02
## [1522,] 0.440355309 0.2596967205 5.105149e-02
## [1523,] 0.293645732 0.0435030714 2.148300e-03
## [1524,] 0.335537578 0.4074384881 1.649156e-01
## [1525,] 0.392899701 0.1042386963 9.218388e-03
## [1526,] 0.163702964 0.4333313752 3.823512e-01
## [1527,] 0.436239133 0.2755194522 5.800410e-02
## [1528,] 0.335537578 0.4074384881 1.649156e-01
## [1529,] 0.444093854 0.2114732637 3.356718e-02
## [1530,] 0.360146521 0.0776786613 5.584740e-03
## [1531,] 0.436239133 0.2755194522 5.800410e-02
## [1532,] 0.407438488 0.3355375785 9.210835e-02
## [1533,] 0.131453291 0.0066840657 1.132892e-04
## [1534,] 0.436239133 0.2755194522 5.800410e-02
## [1535,] 0.386693968 0.3625255950 1.132892e-01
## [1536,] 0.306334128 0.4241549461 1.957638e-01
## [1537,] 0.000000000 0.0000000000 1.000000e+00
## [1538,] 0.442218287 0.1953987782 2.877966e-02
## [1539,] 0.440355309 0.2596967205 5.105149e-02
## [1540,] 0.442218287 0.1953987782 2.877966e-02
## [1541,] 0.306334128 0.4241549461 1.957638e-01
## [1542,] 0.444358195 0.2275981001 3.885821e-02
## [1543,] 0.131453291 0.0066840657 1.132892e-04
## [1544,] 0.227598100 0.4443581954 2.891855e-01
## [1545,] 0.360146521 0.0776786613 5.584740e-03
## [1546,] 0.360146521 0.0776786613 5.584740e-03
## [1547,] 0.416337988 0.3211750193 8.258786e-02
## [1548,] 0.321175019 0.4163379880 1.798991e-01
## [1549,] 0.275519452 0.4362391326 2.302373e-01
## [1550,] 0.131453291 0.0066840657 1.132892e-04
## [1551,] 0.444358195 0.2275981001 3.885821e-02
## [1552,] 0.377630828 0.0906313987 7.250512e-03
## [1553,] 0.436239133 0.2755194522 5.800410e-02
## [1554,] 0.443086838 0.2436977611 4.467792e-02
## [1555,] 0.397531973 0.3493462791 1.023338e-01
## [1556,] 0.430813836 0.2910904300 6.556091e-02
## [1557,] 0.436239133 0.2755194522 5.800410e-02
## [1558,] 0.444358195 0.2275981001 3.885821e-02
## [1559,] 0.362525595 0.3866939680 1.374912e-01
## [1560,] 0.211473264 0.4440938538 3.108657e-01
## [1561,] 0.259696720 0.4403553087 2.488965e-01
## [1562,] 0.444093854 0.2114732637 3.356718e-02
## [1563,] 0.375000000 0.3750000000 1.250000e-01
## [1564,] 0.349346279 0.3975319727 1.507880e-01
## [1565,] 0.417093250 0.1331148669 1.416116e-02
## [1566,] 0.227598100 0.4443581954 2.891855e-01
## [1567,] 0.440355309 0.2596967205 5.105149e-02
## [1568,] 0.417093250 0.1331148669 1.416116e-02
## [1569,] 0.340371253 0.0654560102 4.195898e-03
## [1570,] 0.375000000 0.3750000000 1.250000e-01
## [1571,] 0.293645732 0.0435030714 2.148300e-03
## [1572,] 0.169380014 0.0116813803 2.685375e-04
## [1573,] 0.397531973 0.3493462791 1.023338e-01
## [1574,] 0.227598100 0.4443581954 2.891855e-01
## [1575,] 0.416337988 0.3211750193 8.258786e-02
## [1576,] 0.444358195 0.2275981001 3.885821e-02
## [1577,] 0.438655970 0.1794501695 2.447048e-02
## [1578,] 0.195398778 0.4422182874 3.336033e-01
## [1579,] 0.426168977 0.1482326877 1.718640e-02
## [1580,] 0.335537578 0.4074384881 1.649156e-01
## [1581,] 0.417093250 0.1331148669 1.416116e-02
## [1582,] 0.438655970 0.1794501695 2.447048e-02
## [1583,] 0.444358195 0.2275981001 3.885821e-02
## [1584,] 0.227598100 0.4443581954 2.891855e-01
## [1585,] 0.443086838 0.2436977611 4.467792e-02
## [1586,] 0.375000000 0.3750000000 1.250000e-01
## [1587,] 0.444358195 0.2275981001 3.885821e-02
## [1588,] 0.443086838 0.2436977611 4.467792e-02
## [1589,] 0.204487093 0.0179374643 5.244873e-04
## [1590,] 0.046838810 0.0007678494 4.195898e-06
## [1591,] 0.397531973 0.3493462791 1.023338e-01
## [1592,] 0.430813836 0.2910904300 6.556091e-02
## [1593,] 0.443086838 0.2436977611 4.467792e-02
## [1594,] 0.444093854 0.2114732637 3.356718e-02
## [1595,] 0.163702964 0.4333313752 3.823512e-01
## [1596,] 0.416337988 0.3211750193 8.258786e-02
## [1597,] 0.442218287 0.1953987782 2.877966e-02
## [1598,] 0.440355309 0.2596967205 5.105149e-02
## [1599,] 0.416337988 0.3211750193 8.258786e-02
## [1600,] 0.169380014 0.0116813803 2.685375e-04
## [1601,] 0.243697761 0.4430868383 2.685375e-01
## [1602,] 0.424154946 0.3063341278 7.374710e-02
## [1603,] 0.443086838 0.2436977611 4.467792e-02
## [1604,] 0.417093250 0.1331148669 1.416116e-02
## [1605,] 0.433331375 0.1637029640 2.061445e-02
## [1606,] 0.163702964 0.4333313752 3.823512e-01
## [1607,] 0.440355309 0.2596967205 5.105149e-02
## [1608,] 0.416337988 0.3211750193 8.258786e-02
## [1609,] 0.433331375 0.1637029640 2.061445e-02
## [1610,] 0.335537578 0.4074384881 1.649156e-01
## [1611,] 0.397531973 0.3493462791 1.023338e-01
## [1612,] 0.443086838 0.2436977611 4.467792e-02
## [1613,] 0.386693968 0.3625255950 1.132892e-01
## [1614,] 0.360146521 0.0776786613 5.584740e-03
## [1615,] 0.375000000 0.3750000000 1.250000e-01
## [1616,] 0.406028666 0.1184250277 1.151354e-02
## [1617,] 0.440355309 0.2596967205 5.105149e-02
## [1618,] 0.243697761 0.4430868383 2.685375e-01
## [1619,] 0.440355309 0.2596967205 5.105149e-02
## [1620,] 0.426168977 0.1482326877 1.718640e-02
## [1621,] 0.430813836 0.2910904300 6.556091e-02
## [1622,] 0.407438488 0.3355375785 9.210835e-02
## [1623,] 0.433331375 0.1637029640 2.061445e-02
## [1624,] 0.436239133 0.2755194522 5.800410e-02
## [1625,] 0.397531973 0.3493462791 1.023338e-01
## [1626,] 0.416337988 0.3211750193 8.258786e-02
## [1627,] 0.426168977 0.1482326877 1.718640e-02
## [1628,] 0.259696720 0.4403553087 2.488965e-01
## [1629,] 0.349346279 0.3975319727 1.507880e-01
## [1630,] 0.318229499 0.0540389715 3.058810e-03
## [1631,] 0.426168977 0.1482326877 1.718640e-02
## [1632,] 0.386693968 0.3625255950 1.132892e-01
## [1633,] 0.204487093 0.0179374643 5.244873e-04
## [1634,] 0.440355309 0.2596967205 5.105149e-02
## [1635,] 0.375000000 0.3750000000 1.250000e-01
## [1636,] 0.397531973 0.3493462791 1.023338e-01
## [1637,] 0.362525595 0.3866939680 1.374912e-01
## [1638,] 0.291090430 0.4308138364 2.125348e-01
## [1639,] 0.416337988 0.3211750193 8.258786e-02
## [1640,] 0.169380014 0.0116813803 2.685375e-04
## [1641,] 0.436239133 0.2755194522 5.800410e-02
## [1642,] 0.397531973 0.3493462791 1.023338e-01
## [1643,] 0.386693968 0.3625255950 1.132892e-01
## [1644,] 0.349346279 0.3975319727 1.507880e-01
## [1645,] 0.243697761 0.4430868383 2.685375e-01
## [1646,] 0.406028666 0.1184250277 1.151354e-02
## [1647,] 0.375000000 0.3750000000 1.250000e-01
## [1648,] 0.033923836 0.2665444262 6.980925e-01
## [1649,] 0.000000000 0.0000000000 0.000000e+00
## [1650,] 0.340371253 0.0654560102 4.195898e-03
## [1651,] 0.349346279 0.3975319727 1.507880e-01
## [1652,] 0.424154946 0.3063341278 7.374710e-02
## [1653,] 0.424154946 0.3063341278 7.374710e-02
## [1654,] 0.386693968 0.3625255950 1.132892e-01
## [1655,] 0.179450170 0.4386559699 3.574234e-01
## [1656,] 0.306334128 0.4241549461 1.957638e-01
## [1657,] 0.386693968 0.3625255950 1.132892e-01
## [1658,] 0.033923836 0.2665444262 6.980925e-01
## [1659,] 0.377630828 0.0906313987 7.250512e-03
## [1660,] 0.440355309 0.2596967205 5.105149e-02
## [1661,] 0.443086838 0.2436977611 4.467792e-02
## [1662,] 0.306334128 0.4241549461 1.957638e-01
## [1663,] 0.417093250 0.1331148669 1.416116e-02
## [1664,] 0.392899701 0.1042386963 9.218388e-03
## [1665,] 0.416337988 0.3211750193 8.258786e-02
## [1666,] 0.443086838 0.2436977611 4.467792e-02
## [1667,] 0.392899701 0.1042386963 9.218388e-03
## [1668,] 0.046838810 0.0007678494 4.195898e-06
## [1669,] 0.430813836 0.2910904300 6.556091e-02
## [1670,] 0.275519452 0.4362391326 2.302373e-01
## [1671,] 0.375000000 0.3750000000 1.250000e-01
## [1672,] 0.436239133 0.2755194522 5.800410e-02
## [1673,] 0.318229499 0.0540389715 3.058810e-03
## [1674,] 0.426168977 0.1482326877 1.718640e-02
## [1675,] 0.397531973 0.3493462791 1.023338e-01
## [1676,] 0.433331375 0.1637029640 2.061445e-02
## [1677,] 0.417093250 0.1331148669 1.416116e-02
## [1678,] 0.433331375 0.1637029640 2.061445e-02
## [1679,] 0.443086838 0.2436977611 4.467792e-02
## [1680,] 0.321175019 0.4163379880 1.798991e-01
## [1681,] 0.426168977 0.1482326877 1.718640e-02
## [1682,] 0.407438488 0.3355375785 9.210835e-02
## [1683,] 0.424154946 0.3063341278 7.374710e-02
## [1684,] 0.444093854 0.2114732637 3.356718e-02
## [1685,] 0.438655970 0.1794501695 2.447048e-02
## [1686,] 0.318229499 0.0540389715 3.058810e-03
## [1687,] 0.417093250 0.1331148669 1.416116e-02
## [1688,] 0.275519452 0.4362391326 2.302373e-01
## [1689,] 0.417093250 0.1331148669 1.416116e-02
## [1690,] 0.406028666 0.1184250277 1.151354e-02
## [1691,] 0.444358195 0.2275981001 3.885821e-02
## [1692,] 0.321175019 0.4163379880 1.798991e-01
## [1693,] 0.438655970 0.1794501695 2.447048e-02
## [1694,] 0.443086838 0.2436977611 4.467792e-02
## [1695,] 0.349346279 0.3975319727 1.507880e-01
## [1696,] 0.443086838 0.2436977611 4.467792e-02
## [1697,] 0.275519452 0.4362391326 2.302373e-01
## [1698,] 0.362525595 0.3866939680 1.374912e-01
## [1699,] 0.375000000 0.3750000000 1.250000e-01
## [1700,] 0.406028666 0.1184250277 1.151354e-02
## [1701,] 0.386693968 0.3625255950 1.132892e-01
## [1702,] 0.406028666 0.1184250277 1.151354e-02
## [1703,] 0.377630828 0.0906313987 7.250512e-03
## [1704,] 0.377630828 0.0906313987 7.250512e-03
## [1705,] 0.417093250 0.1331148669 1.416116e-02
## [1706,] 0.275519452 0.4362391326 2.302373e-01
## [1707,] 0.407438488 0.3355375785 9.210835e-02
## [1708,] 0.375000000 0.3750000000 1.250000e-01
## [1709,] 0.236850055 0.0253767916 9.063140e-04
## [1710,] 0.386693968 0.3625255950 1.132892e-01
## [1711,] 0.321175019 0.4163379880 1.798991e-01
## [1712,] 0.426168977 0.1482326877 1.718640e-02
## [1713,] 0.275519452 0.4362391326 2.302373e-01
## [1714,] 0.443086838 0.2436977611 4.467792e-02
## [1715,] 0.266544426 0.0339238361 1.439193e-03
## [1716,] 0.433331375 0.1637029640 2.061445e-02
## [1717,] 0.443086838 0.2436977611 4.467792e-02
## [1718,] 0.362525595 0.3866939680 1.374912e-01
## [1719,] 0.386693968 0.3625255950 1.132892e-01
## [1720,] 0.443086838 0.2436977611 4.467792e-02
## [1721,] 0.416337988 0.3211750193 8.258786e-02
## [1722,] 0.377630828 0.0906313987 7.250512e-03
## [1723,] 0.426168977 0.1482326877 1.718640e-02
## [1724,] 0.406028666 0.1184250277 1.151354e-02
## [1725,] 0.321175019 0.4163379880 1.798991e-01
## [1726,] 0.406028666 0.1184250277 1.151354e-02
## [1727,] 0.444358195 0.2275981001 3.885821e-02
## [1728,] 0.349346279 0.3975319727 1.507880e-01
## [1729,] 0.118425028 0.4060286664 4.640328e-01
## [1730,] 0.438655970 0.1794501695 2.447048e-02
## [1731,] 0.416337988 0.3211750193 8.258786e-02
## [1732,] 0.442218287 0.1953987782 2.877966e-02
## [1733,] 0.375000000 0.3750000000 1.250000e-01
## [1734,] 0.321175019 0.4163379880 1.798991e-01
## [1735,] 0.118425028 0.4060286664 4.640328e-01
## [1736,] 0.243697761 0.4430868383 2.685375e-01
## [1737,] 0.306334128 0.4241549461 1.957638e-01
## [1738,] 0.236850055 0.0253767916 9.063140e-04
## [1739,] 0.179450170 0.4386559699 3.574234e-01
## [1740,] 0.163702964 0.4333313752 3.823512e-01
## [1741,] 0.416337988 0.3211750193 8.258786e-02
## [1742,] 0.204487093 0.0179374643 5.244873e-04
## [1743,] 0.392899701 0.1042386963 9.218388e-03
## [1744,] 0.424154946 0.3063341278 7.374710e-02
## [1745,] 0.430813836 0.2910904300 6.556091e-02
## [1746,] 0.386693968 0.3625255950 1.132892e-01
## [1747,] 0.291090430 0.4308138364 2.125348e-01
## [1748,] 0.416337988 0.3211750193 8.258786e-02
## [1749,] 0.386693968 0.3625255950 1.132892e-01
## [1750,] 0.163702964 0.4333313752 3.823512e-01
## [1751,] 0.259696720 0.4403553087 2.488965e-01
## [1752,] 0.077678661 0.3601465208 5.565901e-01
## [1753,] 0.392899701 0.1042386963 9.218388e-03
## [1754,] 0.430813836 0.2910904300 6.556091e-02
## [1755,] 0.046838810 0.0007678494 4.195898e-06
## [1756,] 0.424154946 0.3063341278 7.374710e-02
## [1757,] 0.360146521 0.0776786613 5.584740e-03
## [1758,] 0.293645732 0.0435030714 2.148300e-03
## [1759,] 0.442218287 0.1953987782 2.877966e-02
## [1760,] 0.377630828 0.0906313987 7.250512e-03
## [1761,] 0.424154946 0.3063341278 7.374710e-02
## [1762,] 0.386693968 0.3625255950 1.132892e-01
## [1763,] 0.442218287 0.1953987782 2.877966e-02
## [1764,] 0.377630828 0.0906313987 7.250512e-03
## [1765,] 0.407438488 0.3355375785 9.210835e-02
## [1766,] 0.442218287 0.1953987782 2.877966e-02
## [1767,] 0.243697761 0.4430868383 2.685375e-01
## [1768,] 0.335537578 0.4074384881 1.649156e-01
## [1769,] 0.436239133 0.2755194522 5.800410e-02
## [1770,] 0.407438488 0.3355375785 9.210835e-02
## [1771,] 0.430813836 0.2910904300 6.556091e-02
## [1772,] 0.438655970 0.1794501695 2.447048e-02
## [1773,] 0.443086838 0.2436977611 4.467792e-02
## [1774,] 0.090631399 0.0030210466 3.356718e-05
## [1775,] 0.406028666 0.1184250277 1.151354e-02
## [1776,] 0.392899701 0.1042386963 9.218388e-03
## [1777,] 0.340371253 0.0654560102 4.195898e-03
## [1778,] 0.440355309 0.2596967205 5.105149e-02
## [1779,] 0.436239133 0.2755194522 5.800410e-02
## [1780,] 0.046838810 0.0007678494 4.195898e-06
## [1781,] 0.148232688 0.4261689772 4.084119e-01
## [1782,] 0.442218287 0.1953987782 2.877966e-02
## [1783,] 0.236850055 0.0253767916 9.063140e-04
## [1784,] 0.293645732 0.0435030714 2.148300e-03
## [1785,] 0.424154946 0.3063341278 7.374710e-02
## [1786,] 0.444358195 0.2275981001 3.885821e-02
## [1787,] 0.321175019 0.4163379880 1.798991e-01
## [1788,] 0.436239133 0.2755194522 5.800410e-02
## [1789,] 0.424154946 0.3063341278 7.374710e-02
## [1790,] 0.266544426 0.0339238361 1.439193e-03
## [1791,] 0.407438488 0.3355375785 9.210835e-02
## [1792,] 0.377630828 0.0906313987 7.250512e-03
## [1793,] 0.444093854 0.2114732637 3.356718e-02
## [1794,] 0.362525595 0.3866939680 1.374912e-01
## [1795,] 0.204487093 0.0179374643 5.244873e-04
## [1796,] 0.407438488 0.3355375785 9.210835e-02
## [1797,] 0.195398778 0.4422182874 3.336033e-01
## [1798,] 0.227598100 0.4443581954 2.891855e-01
## [1799,] 0.259696720 0.4403553087 2.488965e-01
## [1800,] 0.266544426 0.0339238361 1.439193e-03
## [1801,] 0.386693968 0.3625255950 1.132892e-01
## [1802,] 0.335537578 0.4074384881 1.649156e-01
## [1803,] 0.424154946 0.3063341278 7.374710e-02
## [1804,] 0.443086838 0.2436977611 4.467792e-02
## [1805,] 0.430813836 0.2910904300 6.556091e-02
## [1806,] 0.430813836 0.2910904300 6.556091e-02
## [1807,] 0.436239133 0.2755194522 5.800410e-02
## [1808,] 0.438655970 0.1794501695 2.447048e-02
## [1809,] 0.438655970 0.1794501695 2.447048e-02
## [1810,] 0.054038972 0.3182294988 6.246727e-01
## [1811,] 0.090631399 0.0030210466 3.356718e-05
## [1812,] 0.204487093 0.0179374643 5.244873e-04
## [1813,] 0.436239133 0.2755194522 5.800410e-02
## [1814,] 0.440355309 0.2596967205 5.105149e-02
## [1815,] 0.318229499 0.0540389715 3.058810e-03
## [1816,] 0.360146521 0.0776786613 5.584740e-03
## [1817,] 0.169380014 0.0116813803 2.685375e-04
## [1818,] 0.444358195 0.2275981001 3.885821e-02
## [1819,] 0.362525595 0.3866939680 1.374912e-01
## [1820,] 0.436239133 0.2755194522 5.800410e-02
## [1821,] 0.444093854 0.2114732637 3.356718e-02
## [1822,] 0.291090430 0.4308138364 2.125348e-01
## [1823,] 0.397531973 0.3493462791 1.023338e-01
## [1824,] 0.335537578 0.4074384881 1.649156e-01
## [1825,] 0.275519452 0.4362391326 2.302373e-01
## [1826,] 0.377630828 0.0906313987 7.250512e-03
## [1827,] 0.407438488 0.3355375785 9.210835e-02
## [1828,] 0.430813836 0.2910904300 6.556091e-02
## [1829,] 0.077678661 0.3601465208 5.565901e-01
## [1830,] 0.090631399 0.3776308281 5.244873e-01
## [1831,] 0.444358195 0.2275981001 3.885821e-02
## [1832,] 0.118425028 0.4060286664 4.640328e-01
## [1833,] 0.377630828 0.0906313987 7.250512e-03
## [1834,] 0.375000000 0.3750000000 1.250000e-01
## [1835,] 0.306334128 0.4241549461 1.957638e-01
## [1836,] 0.386693968 0.3625255950 1.132892e-01
## [1837,] 0.442218287 0.1953987782 2.877966e-02
## [1838,] 0.407438488 0.3355375785 9.210835e-02
## [1839,] 0.321175019 0.4163379880 1.798991e-01
## [1840,] 0.000000000 0.0000000000 0.000000e+00
## [1841,] 0.375000000 0.3750000000 1.250000e-01
## [1842,] 0.444358195 0.2275981001 3.885821e-02
## [1843,] 0.443086838 0.2436977611 4.467792e-02
## [1844,] 0.442218287 0.1953987782 2.877966e-02
## [1845,] 0.236850055 0.0253767916 9.063140e-04
## [1846,] 0.433331375 0.1637029640 2.061445e-02
## [1847,] 0.424154946 0.3063341278 7.374710e-02
## [1848,] 0.443086838 0.2436977611 4.467792e-02
## [1849,] 0.444358195 0.2275981001 3.885821e-02
## [1850,] 0.436239133 0.2755194522 5.800410e-02
## [1851,] 0.442218287 0.1953987782 2.877966e-02
## [1852,] 0.243697761 0.4430868383 2.685375e-01
## [1853,] 0.443086838 0.2436977611 4.467792e-02
## [1854,] 0.318229499 0.0540389715 3.058810e-03
## [1855,] 0.392899701 0.1042386963 9.218388e-03
## [1856,] 0.424154946 0.3063341278 7.374710e-02
## [1857,] 0.444093854 0.2114732637 3.356718e-02
## [1858,] 0.440355309 0.2596967205 5.105149e-02
## [1859,] 0.291090430 0.4308138364 2.125348e-01
## [1860,] 0.444093854 0.2114732637 3.356718e-02
## [1861,] 0.417093250 0.1331148669 1.416116e-02
## [1862,] 0.430813836 0.2910904300 6.556091e-02
## [1863,] 0.266544426 0.0339238361 1.439193e-03
## [1864,] 0.443086838 0.2436977611 4.467792e-02
## [1865,] 0.430813836 0.2910904300 6.556091e-02
## [1866,] 0.436239133 0.2755194522 5.800410e-02
## [1867,] 0.444093854 0.2114732637 3.356718e-02
## [1868,] 0.424154946 0.3063341278 7.374710e-02
## [1869,] 0.046838810 0.0007678494 4.195898e-06
## [1870,] 0.424154946 0.3063341278 7.374710e-02
## [1871,] 0.406028666 0.1184250277 1.151354e-02
## [1872,] 0.433331375 0.1637029640 2.061445e-02
## [1873,] 0.426168977 0.1482326877 1.718640e-02
## [1874,] 0.211473264 0.4440938538 3.108657e-01
## [1875,] 0.306334128 0.4241549461 1.957638e-01
## [1876,] 0.392899701 0.1042386963 9.218388e-03
## [1877,] 0.397531973 0.3493462791 1.023338e-01
## [1878,] 0.433331375 0.1637029640 2.061445e-02
## [1879,] 0.433331375 0.1637029640 2.061445e-02
## [1880,] 0.442218287 0.1953987782 2.877966e-02
## [1881,] 0.318229499 0.0540389715 3.058810e-03
## [1882,] 0.148232688 0.4261689772 4.084119e-01
## [1883,] 0.335537578 0.4074384881 1.649156e-01
## [1884,] 0.293645732 0.0435030714 2.148300e-03
## [1885,] 0.440355309 0.2596967205 5.105149e-02
## [1886,] 0.169380014 0.0116813803 2.685375e-04
## [1887,] 0.407438488 0.3355375785 9.210835e-02
## [1888,] 0.444358195 0.2275981001 3.885821e-02
## [1889,] 0.204487093 0.0179374643 5.244873e-04
## [1890,] 0.375000000 0.3750000000 1.250000e-01
## [1891,] 0.424154946 0.3063341278 7.374710e-02
## [1892,] 0.090631399 0.0030210466 3.356718e-05
## [1893,] 0.430813836 0.2910904300 6.556091e-02
## [1894,] 0.436239133 0.2755194522 5.800410e-02
## [1895,] 0.417093250 0.1331148669 1.416116e-02
## [1896,] 0.179450170 0.4386559699 3.574234e-01
## [1897,] 0.430813836 0.2910904300 6.556091e-02
## [1898,] 0.407438488 0.3355375785 9.210835e-02
## [1899,] 0.000000000 0.0000000000 0.000000e+00
## [1900,] 0.430813836 0.2910904300 6.556091e-02
## [1901,] 0.424154946 0.3063341278 7.374710e-02
## [1902,] 0.204487093 0.0179374643 5.244873e-04
## [1903,] 0.438655970 0.1794501695 2.447048e-02
## [1904,] 0.443086838 0.2436977611 4.467792e-02
## [1905,] 0.293645732 0.0435030714 2.148300e-03
## [1906,] 0.293645732 0.0435030714 2.148300e-03
## [1907,] 0.397531973 0.3493462791 1.023338e-01
## [1908,] 0.243697761 0.4430868383 2.685375e-01
## [1909,] 0.259696720 0.4403553087 2.488965e-01
## [1910,] 0.377630828 0.0906313987 7.250512e-03
## [1911,] 0.424154946 0.3063341278 7.374710e-02
## [1912,] 0.360146521 0.0776786613 5.584740e-03
## [1913,] 0.442218287 0.1953987782 2.877966e-02
## [1914,] 0.426168977 0.1482326877 1.718640e-02
## [1915,] 0.362525595 0.3866939680 1.374912e-01
## [1916,] 0.444093854 0.2114732637 3.356718e-02
## [1917,] 0.291090430 0.4308138364 2.125348e-01
## [1918,] 0.444358195 0.2275981001 3.885821e-02
## [1919,] 0.291090430 0.4308138364 2.125348e-01
## [1920,] 0.436239133 0.2755194522 5.800410e-02
## [1921,] 0.444358195 0.2275981001 3.885821e-02
## [1922,] 0.397531973 0.3493462791 1.023338e-01
## [1923,] 0.443086838 0.2436977611 4.467792e-02
## [1924,] 0.349346279 0.3975319727 1.507880e-01
## [1925,] 0.340371253 0.0654560102 4.195898e-03
## [1926,] 0.321175019 0.4163379880 1.798991e-01
## [1927,] 0.306334128 0.4241549461 1.957638e-01
## [1928,] 0.349346279 0.3975319727 1.507880e-01
## [1929,] 0.417093250 0.1331148669 1.416116e-02
## [1930,] 0.291090430 0.4308138364 2.125348e-01
## [1931,] 0.424154946 0.3063341278 7.374710e-02
## [1932,] 0.443086838 0.2436977611 4.467792e-02
## [1933,] 0.293645732 0.0435030714 2.148300e-03
## [1934,] 0.430813836 0.2910904300 6.556091e-02
## [1935,] 0.430813836 0.2910904300 6.556091e-02
## [1936,] 0.424154946 0.3063341278 7.374710e-02
## [1937,] 0.426168977 0.1482326877 1.718640e-02
## [1938,] 0.349346279 0.3975319727 1.507880e-01
## [1939,] 0.436239133 0.2755194522 5.800410e-02
## [1940,] 0.211473264 0.4440938538 3.108657e-01
## [1941,] 0.438655970 0.1794501695 2.447048e-02
## [1942,] 0.211473264 0.4440938538 3.108657e-01
## [1943,] 0.169380014 0.0116813803 2.685375e-04
## [1944,] 0.440355309 0.2596967205 5.105149e-02
## [1945,] 0.275519452 0.4362391326 2.302373e-01
## [1946,] 0.375000000 0.3750000000 1.250000e-01
## [1947,] 0.416337988 0.3211750193 8.258786e-02
## [1948,] 0.335537578 0.4074384881 1.649156e-01
## [1949,] 0.377630828 0.0906313987 7.250512e-03
## [1950,] 0.360146521 0.0776786613 5.584740e-03
## [1951,] 0.204487093 0.0179374643 5.244873e-04
## [1952,] 0.386693968 0.3625255950 1.132892e-01
## [1953,] 0.424154946 0.3063341278 7.374710e-02
## [1954,] 0.179450170 0.4386559699 3.574234e-01
## [1955,] 0.417093250 0.1331148669 1.416116e-02
## [1956,] 0.349346279 0.3975319727 1.507880e-01
## [1957,] 0.204487093 0.0179374643 5.244873e-04
## [1958,] 0.397531973 0.3493462791 1.023338e-01
## [1959,] 0.426168977 0.1482326877 1.718640e-02
## [1960,] 0.426168977 0.1482326877 1.718640e-02
## [1961,] 0.430813836 0.2910904300 6.556091e-02
## [1962,] 0.443086838 0.2436977611 4.467792e-02
## [1963,] 0.321175019 0.4163379880 1.798991e-01
## [1964,] 0.406028666 0.1184250277 1.151354e-02
## [1965,] 0.386693968 0.3625255950 1.132892e-01
## [1966,] 0.443086838 0.2436977611 4.467792e-02
## [1967,] 0.430813836 0.2910904300 6.556091e-02
## [1968,] 0.275519452 0.4362391326 2.302373e-01
## [1969,] 0.291090430 0.4308138364 2.125348e-01
## [1970,] 0.444093854 0.2114732637 3.356718e-02
## [1971,] 0.443086838 0.2436977611 4.467792e-02
## [1972,] 0.444358195 0.2275981001 3.885821e-02
## [1973,] 0.362525595 0.3866939680 1.374912e-01
## [1974,] 0.377630828 0.0906313987 7.250512e-03
## [1975,] 0.275519452 0.4362391326 2.302373e-01
## [1976,] 0.430813836 0.2910904300 6.556091e-02
## [1977,] 0.430813836 0.2910904300 6.556091e-02
## [1978,] 0.104238696 0.3928997013 4.936432e-01
## [1979,] 0.362525595 0.3866939680 1.374912e-01
## [1980,] 0.227598100 0.4443581954 2.891855e-01
## [1981,] 0.349346279 0.3975319727 1.507880e-01
## [1982,] 0.306334128 0.4241549461 1.957638e-01
## [1983,] 0.025376792 0.2368500554 7.368668e-01
## [1984,] 0.335537578 0.4074384881 1.649156e-01
## [1985,] 0.442218287 0.1953987782 2.877966e-02
## [1986,] 0.266544426 0.0339238361 1.439193e-03
## [1987,] 0.118425028 0.4060286664 4.640328e-01
## [1988,] 0.397531973 0.3493462791 1.023338e-01
## [1989,] 0.424154946 0.3063341278 7.374710e-02
## [1990,] 0.442218287 0.1953987782 2.877966e-02
## [1991,] 0.406028666 0.1184250277 1.151354e-02
## [1992,] 0.430813836 0.2910904300 6.556091e-02
## [1993,] 0.293645732 0.0435030714 2.148300e-03
## [1994,] 0.444358195 0.2275981001 3.885821e-02
## [1995,] 0.416337988 0.3211750193 8.258786e-02
## [1996,] 0.443086838 0.2436977611 4.467792e-02
## [1997,] 0.349346279 0.3975319727 1.507880e-01
## [1998,] 0.335537578 0.4074384881 1.649156e-01
## [1999,] 0.430813836 0.2910904300 6.556091e-02
## [2000,] 0.340371253 0.0654560102 4.195898e-03
## [2001,] 0.293645732 0.0435030714 2.148300e-03
## [2002,] 0.416337988 0.3211750193 8.258786e-02
## [2003,] 0.426168977 0.1482326877 1.718640e-02
## [2004,] 0.033923836 0.2665444262 6.980925e-01
## [2005,] 0.392899701 0.1042386963 9.218388e-03
## [2006,] 0.360146521 0.0776786613 5.584740e-03
## [2007,] 0.443086838 0.2436977611 4.467792e-02
## [2008,] 0.436239133 0.2755194522 5.800410e-02
## [2009,] 0.362525595 0.3866939680 1.374912e-01
## [2010,] 0.349346279 0.3975319727 1.507880e-01
## [2011,] 0.266544426 0.0339238361 1.439193e-03
## [2012,] 0.321175019 0.4163379880 1.798991e-01
## [2013,] 0.443086838 0.2436977611 4.467792e-02
## [2014,] 0.424154946 0.3063341278 7.374710e-02
## [2015,] 0.417093250 0.1331148669 1.416116e-02
## [2016,] 0.360146521 0.0776786613 5.584740e-03
## [2017,] 0.318229499 0.0540389715 3.058810e-03
## [2018,] 0.443086838 0.2436977611 4.467792e-02
## [2019,] 0.438655970 0.1794501695 2.447048e-02
## [2020,] 0.275519452 0.4362391326 2.302373e-01
## [2021,] 0.426168977 0.1482326877 1.718640e-02
## [2022,] 0.195398778 0.4422182874 3.336033e-01
## [2023,] 0.444093854 0.2114732637 3.356718e-02
## [2024,] 0.291090430 0.4308138364 2.125348e-01
## [2025,] 0.236850055 0.0253767916 9.063140e-04
## [2026,] 0.169380014 0.0116813803 2.685375e-04
## [2027,] 0.444093854 0.2114732637 3.356718e-02
## [2028,] 0.360146521 0.0776786613 5.584740e-03
## [2029,] 0.377630828 0.0906313987 7.250512e-03
## [2030,] 0.444093854 0.2114732637 3.356718e-02
## [2031,] 0.375000000 0.3750000000 1.250000e-01
## [2032,] 0.054038972 0.3182294988 6.246727e-01
## [2033,] 0.406028666 0.1184250277 1.151354e-02
## [2034,] 0.406028666 0.1184250277 1.151354e-02
## [2035,] 0.443086838 0.2436977611 4.467792e-02
## [2036,] 0.266544426 0.0339238361 1.439193e-03
## [2037,] 0.438655970 0.1794501695 2.447048e-02
## [2038,] 0.227598100 0.4443581954 2.891855e-01
## [2039,] 0.375000000 0.3750000000 1.250000e-01
## [2040,] 0.436239133 0.2755194522 5.800410e-02
## [2041,] 0.227598100 0.4443581954 2.891855e-01
## [2042,] 0.318229499 0.0540389715 3.058810e-03
## [2043,] 0.377630828 0.0906313987 7.250512e-03
## [2044,] 0.306334128 0.4241549461 1.957638e-01
## [2045,] 0.426168977 0.1482326877 1.718640e-02
## [2046,] 0.397531973 0.3493462791 1.023338e-01
## [2047,] 0.360146521 0.0776786613 5.584740e-03
## [2048,] 0.440355309 0.2596967205 5.105149e-02
## [2049,] 0.377630828 0.0906313987 7.250512e-03
## [2050,] 0.433331375 0.1637029640 2.061445e-02
## [2051,] 0.169380014 0.0116813803 2.685375e-04
## [2052,] 0.442218287 0.1953987782 2.877966e-02
## [2053,] 0.179450170 0.4386559699 3.574234e-01
## [2054,] 0.397531973 0.3493462791 1.023338e-01
## [2055,] 0.349346279 0.3975319727 1.507880e-01
## [2056,] 0.397531973 0.3493462791 1.023338e-01
## [2057,] 0.340371253 0.0654560102 4.195898e-03
## [2058,] 0.436239133 0.2755194522 5.800410e-02
## [2059,] 0.406028666 0.1184250277 1.151354e-02
## [2060,] 0.426168977 0.1482326877 1.718640e-02
## [2061,] 0.444358195 0.2275981001 3.885821e-02
## [2062,] 0.424154946 0.3063341278 7.374710e-02
## [2063,] 0.444093854 0.2114732637 3.356718e-02
## [2064,] 0.386693968 0.3625255950 1.132892e-01
## [2065,] 0.443086838 0.2436977611 4.467792e-02
## [2066,] 0.318229499 0.0540389715 3.058810e-03
## [2067,] 0.436239133 0.2755194522 5.800410e-02
## [2068,] 0.377630828 0.0906313987 7.250512e-03
## [2069,] 0.360146521 0.0776786613 5.584740e-03
## [2070,] 0.386693968 0.3625255950 1.132892e-01
## [2071,] 0.275519452 0.4362391326 2.302373e-01
## [2072,] 0.424154946 0.3063341278 7.374710e-02
## [2073,] 0.266544426 0.0339238361 1.439193e-03
## [2074,] 0.349346279 0.3975319727 1.507880e-01
## [2075,] 0.362525595 0.3866939680 1.374912e-01
## [2076,] 0.426168977 0.1482326877 1.718640e-02
## [2077,] 0.377630828 0.0906313987 7.250512e-03
## [2078,] 0.426168977 0.1482326877 1.718640e-02
## [2079,] 0.436239133 0.2755194522 5.800410e-02
## [2080,] 0.362525595 0.3866939680 1.374912e-01
## [2081,] 0.360146521 0.0776786613 5.584740e-03
## [2082,] 0.169380014 0.0116813803 2.685375e-04
## [2083,] 0.306334128 0.4241549461 1.957638e-01
## [2084,] 0.407438488 0.3355375785 9.210835e-02
## [2085,] 0.433331375 0.1637029640 2.061445e-02
## [2086,] 0.321175019 0.4163379880 1.798991e-01
## [2087,] 0.195398778 0.4422182874 3.336033e-01
## [2088,] 0.443086838 0.2436977611 4.467792e-02
## [2089,] 0.335537578 0.4074384881 1.649156e-01
## [2090,] 0.443086838 0.2436977611 4.467792e-02
## [2091,] 0.275519452 0.4362391326 2.302373e-01
## [2092,] 0.444358195 0.2275981001 3.885821e-02
## [2093,] 0.243697761 0.4430868383 2.685375e-01
## [2094,] 0.349346279 0.3975319727 1.507880e-01
## [2095,] 0.406028666 0.1184250277 1.151354e-02
## [2096,] 0.362525595 0.3866939680 1.374912e-01
## [2097,] 0.293645732 0.0435030714 2.148300e-03
## [2098,] 0.433331375 0.1637029640 2.061445e-02
## [2099,] 0.392899701 0.1042386963 9.218388e-03
## [2100,] 0.318229499 0.0540389715 3.058810e-03
## [2101,] 0.318229499 0.0540389715 3.058810e-03
## [2102,] 0.291090430 0.4308138364 2.125348e-01
## attr(,"degree")
## [1] 3
## attr(,"knots")
## numeric(0)
## attr(,"Boundary.knots")
## [1] 18 80
## attr(,"intercept")
## [1] FALSE
## attr(,"class")
## [1] "bs"     "basis"  "matrix"

#  So in this case, we pass at a single variable, in this case, the training set, we take the age variable, and we say we want a third degree polynomial for this variable. So when you do that, you essentially get, you'll get a three-column matrix out. So this is now three new variables. This variable corresponds to age, the actual age values. There are scales for computational purposes.
# The second column will correspond to something like age squared. So, in other words, you're allowing it to fit a quadratic relationship between age and the outcome. And the third column will correspond to age cubed, so you allow a cubic relationship between age and the outcome. So this'll, if you include these covariates in the model instead of just the age variable when you're fitting a linear regression, you allow for curvy model fitting. 

# fitting curves with splines
lm1 <- lm(wage ~bsBasis, data=training)
plot(training$age, training$wage, pch=19, cex=0.5)

# points(training$age, predict(lm1, newdata=training), col="red", pch=19, cex=0.5)

# splines on the test set
predict(bsBasis, age=testing$age)

##                   1            2            3
##    [1,] 0.000000000 0.0000000000 0.000000e+00
##    [2,] 0.236850055 0.0253767916 9.063140e-04
##    [3,] 0.416337988 0.3211750193 8.258786e-02
##    [4,] 0.430813836 0.2910904300 6.556091e-02
##    [5,] 0.306334128 0.4241549461 1.957638e-01
##    [6,] 0.424154946 0.3063341278 7.374710e-02
##    [7,] 0.377630828 0.0906313987 7.250512e-03
##    [8,] 0.440355309 0.2596967205 5.105149e-02
##    [9,] 0.335537578 0.4074384881 1.649156e-01
##   [10,] 0.416337988 0.3211750193 8.258786e-02
##   [11,] 0.433331375 0.1637029640 2.061445e-02
##   [12,] 0.444358195 0.2275981001 3.885821e-02
##   [13,] 0.306334128 0.4241549461 1.957638e-01
##   [14,] 0.442218287 0.1953987782 2.877966e-02
##   [15,] 0.275519452 0.4362391326 2.302373e-01
##   [16,] 0.444093854 0.2114732637 3.356718e-02
##   [17,] 0.443086838 0.2436977611 4.467792e-02
##   [18,] 0.443086838 0.2436977611 4.467792e-02
##   [19,] 0.444093854 0.2114732637 3.356718e-02
##   [20,] 0.375000000 0.3750000000 1.250000e-01
##   [21,] 0.430813836 0.2910904300 6.556091e-02
##   [22,] 0.426168977 0.1482326877 1.718640e-02
##   [23,] 0.259696720 0.4403553087 2.488965e-01
##   [24,] 0.000000000 0.0000000000 0.000000e+00
##   [25,] 0.291090430 0.4308138364 2.125348e-01
##   [26,] 0.417093250 0.1331148669 1.416116e-02
##   [27,] 0.438655970 0.1794501695 2.447048e-02
##   [28,] 0.275519452 0.4362391326 2.302373e-01
##   [29,] 0.065456010 0.3403712531 5.899768e-01
##   [30,] 0.266544426 0.0339238361 1.439193e-03
##   [31,] 0.406028666 0.1184250277 1.151354e-02
##   [32,] 0.430813836 0.2910904300 6.556091e-02
##   [33,] 0.444358195 0.2275981001 3.885821e-02
##   [34,] 0.335537578 0.4074384881 1.649156e-01
##   [35,] 0.266544426 0.0339238361 1.439193e-03
##   [36,] 0.417093250 0.1331148669 1.416116e-02
##   [37,] 0.259696720 0.4403553087 2.488965e-01
##   [38,] 0.054038972 0.3182294988 6.246727e-01
##   [39,] 0.204487093 0.0179374643 5.244873e-04
##   [40,] 0.377630828 0.0906313987 7.250512e-03
##   [41,] 0.169380014 0.0116813803 2.685375e-04
##   [42,] 0.227598100 0.4443581954 2.891855e-01
##   [43,] 0.340371253 0.0654560102 4.195898e-03
##   [44,] 0.195398778 0.4422182874 3.336033e-01
##   [45,] 0.426168977 0.1482326877 1.718640e-02
##   [46,] 0.430813836 0.2910904300 6.556091e-02
##   [47,] 0.306334128 0.4241549461 1.957638e-01
##   [48,] 0.386693968 0.3625255950 1.132892e-01
##   [49,] 0.375000000 0.3750000000 1.250000e-01
##   [50,] 0.436239133 0.2755194522 5.800410e-02
##   [51,] 0.291090430 0.4308138364 2.125348e-01
##   [52,] 0.131453291 0.0066840657 1.132892e-04
##   [53,] 0.243697761 0.4430868383 2.685375e-01
##   [54,] 0.392899701 0.1042386963 9.218388e-03
##   [55,] 0.266544426 0.0339238361 1.439193e-03
##   [56,] 0.406028666 0.1184250277 1.151354e-02
##   [57,] 0.424154946 0.3063341278 7.374710e-02
##   [58,] 0.211473264 0.4440938538 3.108657e-01
##   [59,] 0.424154946 0.3063341278 7.374710e-02
##   [60,] 0.291090430 0.4308138364 2.125348e-01
##   [61,] 0.266544426 0.0339238361 1.439193e-03
##   [62,] 0.321175019 0.4163379880 1.798991e-01
##   [63,] 0.065456010 0.3403712531 5.899768e-01
##   [64,] 0.397531973 0.3493462791 1.023338e-01
##   [65,] 0.426168977 0.1482326877 1.718640e-02
##   [66,] 0.169380014 0.0116813803 2.685375e-04
##   [67,] 0.416337988 0.3211750193 8.258786e-02
##   [68,] 0.430813836 0.2910904300 6.556091e-02
##   [69,] 0.417093250 0.1331148669 1.416116e-02
##   [70,] 0.179450170 0.4386559699 3.574234e-01
##   [71,] 0.442218287 0.1953987782 2.877966e-02
##   [72,] 0.362525595 0.3866939680 1.374912e-01
##   [73,] 0.440355309 0.2596967205 5.105149e-02
##   [74,] 0.444093854 0.2114732637 3.356718e-02
##   [75,] 0.433331375 0.1637029640 2.061445e-02
##   [76,] 0.360146521 0.0776786613 5.584740e-03
##   [77,] 0.444358195 0.2275981001 3.885821e-02
##   [78,] 0.291090430 0.4308138364 2.125348e-01
##   [79,] 0.444093854 0.2114732637 3.356718e-02
##   [80,] 0.375000000 0.3750000000 1.250000e-01
##   [81,] 0.436239133 0.2755194522 5.800410e-02
##   [82,] 0.430813836 0.2910904300 6.556091e-02
##   [83,] 0.444093854 0.2114732637 3.356718e-02
##   [84,] 0.259696720 0.4403553087 2.488965e-01
##   [85,] 0.266544426 0.0339238361 1.439193e-03
##   [86,] 0.375000000 0.3750000000 1.250000e-01
##   [87,] 0.440355309 0.2596967205 5.105149e-02
##   [88,] 0.375000000 0.3750000000 1.250000e-01
##   [89,] 0.335537578 0.4074384881 1.649156e-01
##   [90,] 0.430813836 0.2910904300 6.556091e-02
##   [91,] 0.211473264 0.4440938538 3.108657e-01
##   [92,] 0.407438488 0.3355375785 9.210835e-02
##   [93,] 0.131453291 0.0066840657 1.132892e-04
##   [94,] 0.195398778 0.4422182874 3.336033e-01
##   [95,] 0.406028666 0.1184250277 1.151354e-02
##   [96,] 0.293645732 0.0435030714 2.148300e-03
##   [97,] 0.406028666 0.1184250277 1.151354e-02
##   [98,] 0.442218287 0.1953987782 2.877966e-02
##   [99,] 0.169380014 0.0116813803 2.685375e-04
##  [100,] 0.424154946 0.3063341278 7.374710e-02
##  [101,] 0.433331375 0.1637029640 2.061445e-02
##  [102,] 0.443086838 0.2436977611 4.467792e-02
##  [103,] 0.433331375 0.1637029640 2.061445e-02
##  [104,] 0.433331375 0.1637029640 2.061445e-02
##  [105,] 0.430813836 0.2910904300 6.556091e-02
##  [106,] 0.417093250 0.1331148669 1.416116e-02
##  [107,] 0.211473264 0.4440938538 3.108657e-01
##  [108,] 0.444093854 0.2114732637 3.356718e-02
##  [109,] 0.321175019 0.4163379880 1.798991e-01
##  [110,] 0.259696720 0.4403553087 2.488965e-01
##  [111,] 0.148232688 0.4261689772 4.084119e-01
##  [112,] 0.433331375 0.1637029640 2.061445e-02
##  [113,] 0.306334128 0.4241549461 1.957638e-01
##  [114,] 0.416337988 0.3211750193 8.258786e-02
##  [115,] 0.386693968 0.3625255950 1.132892e-01
##  [116,] 0.407438488 0.3355375785 9.210835e-02
##  [117,] 0.291090430 0.4308138364 2.125348e-01
##  [118,] 0.375000000 0.3750000000 1.250000e-01
##  [119,] 0.426168977 0.1482326877 1.718640e-02
##  [120,] 0.443086838 0.2436977611 4.467792e-02
##  [121,] 0.442218287 0.1953987782 2.877966e-02
##  [122,] 0.444358195 0.2275981001 3.885821e-02
##  [123,] 0.335537578 0.4074384881 1.649156e-01
##  [124,] 0.362525595 0.3866939680 1.374912e-01
##  [125,] 0.397531973 0.3493462791 1.023338e-01
##  [126,] 0.318229499 0.0540389715 3.058810e-03
##  [127,] 0.424154946 0.3063341278 7.374710e-02
##  [128,] 0.442218287 0.1953987782 2.877966e-02
##  [129,] 0.335537578 0.4074384881 1.649156e-01
##  [130,] 0.444358195 0.2275981001 3.885821e-02
##  [131,] 0.392899701 0.1042386963 9.218388e-03
##  [132,] 0.243697761 0.4430868383 2.685375e-01
##  [133,] 0.377630828 0.0906313987 7.250512e-03
##  [134,] 0.318229499 0.0540389715 3.058810e-03
##  [135,] 0.433331375 0.1637029640 2.061445e-02
##  [136,] 0.386693968 0.3625255950 1.132892e-01
##  [137,] 0.360146521 0.0776786613 5.584740e-03
##  [138,] 0.266544426 0.0339238361 1.439193e-03
##  [139,] 0.443086838 0.2436977611 4.467792e-02
##  [140,] 0.318229499 0.0540389715 3.058810e-03
##  [141,] 0.375000000 0.3750000000 1.250000e-01
##  [142,] 0.169380014 0.0116813803 2.685375e-04
##  [143,] 0.416337988 0.3211750193 8.258786e-02
##  [144,] 0.163702964 0.4333313752 3.823512e-01
##  [145,] 0.375000000 0.3750000000 1.250000e-01
##  [146,] 0.266544426 0.0339238361 1.439193e-03
##  [147,] 0.360146521 0.0776786613 5.584740e-03
##  [148,] 0.442218287 0.1953987782 2.877966e-02
##  [149,] 0.433331375 0.1637029640 2.061445e-02
##  [150,] 0.407438488 0.3355375785 9.210835e-02
##  [151,] 0.243697761 0.4430868383 2.685375e-01
##  [152,] 0.444358195 0.2275981001 3.885821e-02
##  [153,] 0.442218287 0.1953987782 2.877966e-02
##  [154,] 0.318229499 0.0540389715 3.058810e-03
##  [155,] 0.442218287 0.1953987782 2.877966e-02
##  [156,] 0.275519452 0.4362391326 2.302373e-01
##  [157,] 0.438655970 0.1794501695 2.447048e-02
##  [158,] 0.204487093 0.0179374643 5.244873e-04
##  [159,] 0.407438488 0.3355375785 9.210835e-02
##  [160,] 0.306334128 0.4241549461 1.957638e-01
##  [161,] 0.179450170 0.4386559699 3.574234e-01
##  [162,] 0.443086838 0.2436977611 4.467792e-02
##  [163,] 0.321175019 0.4163379880 1.798991e-01
##  [164,] 0.204487093 0.0179374643 5.244873e-04
##  [165,] 0.426168977 0.1482326877 1.718640e-02
##  [166,] 0.430813836 0.2910904300 6.556091e-02
##  [167,] 0.227598100 0.4443581954 2.891855e-01
##  [168,] 0.211473264 0.4440938538 3.108657e-01
##  [169,] 0.375000000 0.3750000000 1.250000e-01
##  [170,] 0.416337988 0.3211750193 8.258786e-02
##  [171,] 0.169380014 0.0116813803 2.685375e-04
##  [172,] 0.438655970 0.1794501695 2.447048e-02
##  [173,] 0.444093854 0.2114732637 3.356718e-02
##  [174,] 0.397531973 0.3493462791 1.023338e-01
##  [175,] 0.433331375 0.1637029640 2.061445e-02
##  [176,] 0.375000000 0.3750000000 1.250000e-01
##  [177,] 0.443086838 0.2436977611 4.467792e-02
##  [178,] 0.406028666 0.1184250277 1.151354e-02
##  [179,] 0.259696720 0.4403553087 2.488965e-01
##  [180,] 0.033923836 0.2665444262 6.980925e-01
##  [181,] 0.375000000 0.3750000000 1.250000e-01
##  [182,] 0.377630828 0.0906313987 7.250512e-03
##  [183,] 0.360146521 0.0776786613 5.584740e-03
##  [184,] 0.444358195 0.2275981001 3.885821e-02
##  [185,] 0.436239133 0.2755194522 5.800410e-02
##  [186,] 0.386693968 0.3625255950 1.132892e-01
##  [187,] 0.424154946 0.3063341278 7.374710e-02
##  [188,] 0.406028666 0.1184250277 1.151354e-02
##  [189,] 0.407438488 0.3355375785 9.210835e-02
##  [190,] 0.335537578 0.4074384881 1.649156e-01
##  [191,] 0.169380014 0.0116813803 2.685375e-04
##  [192,] 0.321175019 0.4163379880 1.798991e-01
##  [193,] 0.426168977 0.1482326877 1.718640e-02
##  [194,] 0.444093854 0.2114732637 3.356718e-02
##  [195,] 0.436239133 0.2755194522 5.800410e-02
##  [196,] 0.266544426 0.0339238361 1.439193e-03
##  [197,] 0.360146521 0.0776786613 5.584740e-03
##  [198,] 0.340371253 0.0654560102 4.195898e-03
##  [199,] 0.407438488 0.3355375785 9.210835e-02
##  [200,] 0.275519452 0.4362391326 2.302373e-01
##  [201,] 0.440355309 0.2596967205 5.105149e-02
##  [202,] 0.195398778 0.4422182874 3.336033e-01
##  [203,] 0.397531973 0.3493462791 1.023338e-01
##  [204,] 0.318229499 0.0540389715 3.058810e-03
##  [205,] 0.243697761 0.4430868383 2.685375e-01
##  [206,] 0.318229499 0.0540389715 3.058810e-03
##  [207,] 0.335537578 0.4074384881 1.649156e-01
##  [208,] 0.416337988 0.3211750193 8.258786e-02
##  [209,] 0.266544426 0.0339238361 1.439193e-03
##  [210,] 0.440355309 0.2596967205 5.105149e-02
##  [211,] 0.306334128 0.4241549461 1.957638e-01
##  [212,] 0.204487093 0.0179374643 5.244873e-04
##  [213,] 0.392899701 0.1042386963 9.218388e-03
##  [214,] 0.335537578 0.4074384881 1.649156e-01
##  [215,] 0.416337988 0.3211750193 8.258786e-02
##  [216,] 0.443086838 0.2436977611 4.467792e-02
##  [217,] 0.417093250 0.1331148669 1.416116e-02
##  [218,] 0.266544426 0.0339238361 1.439193e-03
##  [219,] 0.236850055 0.0253767916 9.063140e-04
##  [220,] 0.236850055 0.0253767916 9.063140e-04
##  [221,] 0.440355309 0.2596967205 5.105149e-02
##  [222,] 0.436239133 0.2755194522 5.800410e-02
##  [223,] 0.291090430 0.4308138364 2.125348e-01
##  [224,] 0.211473264 0.4440938538 3.108657e-01
##  [225,] 0.443086838 0.2436977611 4.467792e-02
##  [226,] 0.440355309 0.2596967205 5.105149e-02
##  [227,] 0.000000000 0.0000000000 1.000000e+00
##  [228,] 0.321175019 0.4163379880 1.798991e-01
##  [229,] 0.443086838 0.2436977611 4.467792e-02
##  [230,] 0.433331375 0.1637029640 2.061445e-02
##  [231,] 0.236850055 0.0253767916 9.063140e-04
##  [232,] 0.377630828 0.0906313987 7.250512e-03
##  [233,] 0.090631399 0.3776308281 5.244873e-01
##  [234,] 0.306334128 0.4241549461 1.957638e-01
##  [235,] 0.318229499 0.0540389715 3.058810e-03
##  [236,] 0.321175019 0.4163379880 1.798991e-01
##  [237,] 0.386693968 0.3625255950 1.132892e-01
##  [238,] 0.227598100 0.4443581954 2.891855e-01
##  [239,] 0.416337988 0.3211750193 8.258786e-02
##  [240,] 0.430813836 0.2910904300 6.556091e-02
##  [241,] 0.377630828 0.0906313987 7.250512e-03
##  [242,] 0.259696720 0.4403553087 2.488965e-01
##  [243,] 0.321175019 0.4163379880 1.798991e-01
##  [244,] 0.436239133 0.2755194522 5.800410e-02
##  [245,] 0.204487093 0.0179374643 5.244873e-04
##  [246,] 0.243697761 0.4430868383 2.685375e-01
##  [247,] 0.430813836 0.2910904300 6.556091e-02
##  [248,] 0.417093250 0.1331148669 1.416116e-02
##  [249,] 0.275519452 0.4362391326 2.302373e-01
##  [250,] 0.442218287 0.1953987782 2.877966e-02
##  [251,] 0.440355309 0.2596967205 5.105149e-02
##  [252,] 0.417093250 0.1331148669 1.416116e-02
##  [253,] 0.362525595 0.3866939680 1.374912e-01
##  [254,] 0.321175019 0.4163379880 1.798991e-01
##  [255,] 0.442218287 0.1953987782 2.877966e-02
##  [256,] 0.090631399 0.0030210466 3.356718e-05
##  [257,] 0.293645732 0.0435030714 2.148300e-03
##  [258,] 0.360146521 0.0776786613 5.584740e-03
##  [259,] 0.397531973 0.3493462791 1.023338e-01
##  [260,] 0.306334128 0.4241549461 1.957638e-01
##  [261,] 0.204487093 0.0179374643 5.244873e-04
##  [262,] 0.430813836 0.2910904300 6.556091e-02
##  [263,] 0.386693968 0.3625255950 1.132892e-01
##  [264,] 0.417093250 0.1331148669 1.416116e-02
##  [265,] 0.335537578 0.4074384881 1.649156e-01
##  [266,] 0.349346279 0.3975319727 1.507880e-01
##  [267,] 0.397531973 0.3493462791 1.023338e-01
##  [268,] 0.340371253 0.0654560102 4.195898e-03
##  [269,] 0.335537578 0.4074384881 1.649156e-01
##  [270,] 0.204487093 0.0179374643 5.244873e-04
##  [271,] 0.133114867 0.4170932496 4.356307e-01
##  [272,] 0.318229499 0.0540389715 3.058810e-03
##  [273,] 0.417093250 0.1331148669 1.416116e-02
##  [274,] 0.375000000 0.3750000000 1.250000e-01
##  [275,] 0.318229499 0.0540389715 3.058810e-03
##  [276,] 0.443086838 0.2436977611 4.467792e-02
##  [277,] 0.407438488 0.3355375785 9.210835e-02
##  [278,] 0.321175019 0.4163379880 1.798991e-01
##  [279,] 0.266544426 0.0339238361 1.439193e-03
##  [280,] 0.433331375 0.1637029640 2.061445e-02
##  [281,] 0.362525595 0.3866939680 1.374912e-01
##  [282,] 0.426168977 0.1482326877 1.718640e-02
##  [283,] 0.386693968 0.3625255950 1.132892e-01
##  [284,] 0.375000000 0.3750000000 1.250000e-01
##  [285,] 0.440355309 0.2596967205 5.105149e-02
##  [286,] 0.442218287 0.1953987782 2.877966e-02
##  [287,] 0.243697761 0.4430868383 2.685375e-01
##  [288,] 0.340371253 0.0654560102 4.195898e-03
##  [289,] 0.417093250 0.1331148669 1.416116e-02
##  [290,] 0.362525595 0.3866939680 1.374912e-01
##  [291,] 0.444093854 0.2114732637 3.356718e-02
##  [292,] 0.375000000 0.3750000000 1.250000e-01
##  [293,] 0.424154946 0.3063341278 7.374710e-02
##  [294,] 0.362525595 0.3866939680 1.374912e-01
##  [295,] 0.416337988 0.3211750193 8.258786e-02
##  [296,] 0.424154946 0.3063341278 7.374710e-02
##  [297,] 0.227598100 0.4443581954 2.891855e-01
##  [298,] 0.349346279 0.3975319727 1.507880e-01
##  [299,] 0.416337988 0.3211750193 8.258786e-02
##  [300,] 0.417093250 0.1331148669 1.416116e-02
##  [301,] 0.416337988 0.3211750193 8.258786e-02
##  [302,] 0.362525595 0.3866939680 1.374912e-01
##  [303,] 0.444358195 0.2275981001 3.885821e-02
##  [304,] 0.375000000 0.3750000000 1.250000e-01
##  [305,] 0.090631399 0.0030210466 3.356718e-05
##  [306,] 0.392899701 0.1042386963 9.218388e-03
##  [307,] 0.375000000 0.3750000000 1.250000e-01
##  [308,] 0.275519452 0.4362391326 2.302373e-01
##  [309,] 0.195398778 0.4422182874 3.336033e-01
##  [310,] 0.275519452 0.4362391326 2.302373e-01
##  [311,] 0.349346279 0.3975319727 1.507880e-01
##  [312,] 0.436239133 0.2755194522 5.800410e-02
##  [313,] 0.416337988 0.3211750193 8.258786e-02
##  [314,] 0.377630828 0.0906313987 7.250512e-03
##  [315,] 0.386693968 0.3625255950 1.132892e-01
##  [316,] 0.417093250 0.1331148669 1.416116e-02
##  [317,] 0.392899701 0.1042386963 9.218388e-03
##  [318,] 0.386693968 0.3625255950 1.132892e-01
##  [319,] 0.433331375 0.1637029640 2.061445e-02
##  [320,] 0.397531973 0.3493462791 1.023338e-01
##  [321,] 0.416337988 0.3211750193 8.258786e-02
##  [322,] 0.335537578 0.4074384881 1.649156e-01
##  [323,] 0.375000000 0.3750000000 1.250000e-01
##  [324,] 0.407438488 0.3355375785 9.210835e-02
##  [325,] 0.430813836 0.2910904300 6.556091e-02
##  [326,] 0.424154946 0.3063341278 7.374710e-02
##  [327,] 0.443086838 0.2436977611 4.467792e-02
##  [328,] 0.417093250 0.1331148669 1.416116e-02
##  [329,] 0.444093854 0.2114732637 3.356718e-02
##  [330,] 0.440355309 0.2596967205 5.105149e-02
##  [331,] 0.377630828 0.0906313987 7.250512e-03
##  [332,] 0.349346279 0.3975319727 1.507880e-01
##  [333,] 0.444358195 0.2275981001 3.885821e-02
##  [334,] 0.433331375 0.1637029640 2.061445e-02
##  [335,] 0.397531973 0.3493462791 1.023338e-01
##  [336,] 0.349346279 0.3975319727 1.507880e-01
##  [337,] 0.440355309 0.2596967205 5.105149e-02
##  [338,] 0.163702964 0.4333313752 3.823512e-01
##  [339,] 0.195398778 0.4422182874 3.336033e-01
##  [340,] 0.407438488 0.3355375785 9.210835e-02
##  [341,] 0.204487093 0.0179374643 5.244873e-04
##  [342,] 0.416337988 0.3211750193 8.258786e-02
##  [343,] 0.163702964 0.4333313752 3.823512e-01
##  [344,] 0.227598100 0.4443581954 2.891855e-01
##  [345,] 0.377630828 0.0906313987 7.250512e-03
##  [346,] 0.416337988 0.3211750193 8.258786e-02
##  [347,] 0.436239133 0.2755194522 5.800410e-02
##  [348,] 0.335537578 0.4074384881 1.649156e-01
##  [349,] 0.306334128 0.4241549461 1.957638e-01
##  [350,] 0.377630828 0.0906313987 7.250512e-03
##  [351,] 0.444093854 0.2114732637 3.356718e-02
##  [352,] 0.444358195 0.2275981001 3.885821e-02
##  [353,] 0.362525595 0.3866939680 1.374912e-01
##  [354,] 0.397531973 0.3493462791 1.023338e-01
##  [355,] 0.416337988 0.3211750193 8.258786e-02
##  [356,] 0.424154946 0.3063341278 7.374710e-02
##  [357,] 0.335537578 0.4074384881 1.649156e-01
##  [358,] 0.436239133 0.2755194522 5.800410e-02
##  [359,] 0.275519452 0.4362391326 2.302373e-01
##  [360,] 0.362525595 0.3866939680 1.374912e-01
##  [361,] 0.321175019 0.4163379880 1.798991e-01
##  [362,] 0.318229499 0.0540389715 3.058810e-03
##  [363,] 0.275519452 0.4362391326 2.302373e-01
##  [364,] 0.362525595 0.3866939680 1.374912e-01
##  [365,] 0.362525595 0.3866939680 1.374912e-01
##  [366,] 0.375000000 0.3750000000 1.250000e-01
##  [367,] 0.436239133 0.2755194522 5.800410e-02
##  [368,] 0.362525595 0.3866939680 1.374912e-01
##  [369,] 0.321175019 0.4163379880 1.798991e-01
##  [370,] 0.340371253 0.0654560102 4.195898e-03
##  [371,] 0.236850055 0.0253767916 9.063140e-04
##  [372,] 0.266544426 0.0339238361 1.439193e-03
##  [373,] 0.444093854 0.2114732637 3.356718e-02
##  [374,] 0.397531973 0.3493462791 1.023338e-01
##  [375,] 0.444093854 0.2114732637 3.356718e-02
##  [376,] 0.444358195 0.2275981001 3.885821e-02
##  [377,] 0.335537578 0.4074384881 1.649156e-01
##  [378,] 0.195398778 0.4422182874 3.336033e-01
##  [379,] 0.195398778 0.4422182874 3.336033e-01
##  [380,] 0.318229499 0.0540389715 3.058810e-03
##  [381,] 0.416337988 0.3211750193 8.258786e-02
##  [382,] 0.243697761 0.4430868383 2.685375e-01
##  [383,] 0.426168977 0.1482326877 1.718640e-02
##  [384,] 0.443086838 0.2436977611 4.467792e-02
##  [385,] 0.349346279 0.3975319727 1.507880e-01
##  [386,] 0.362525595 0.3866939680 1.374912e-01
##  [387,] 0.148232688 0.4261689772 4.084119e-01
##  [388,] 0.306334128 0.4241549461 1.957638e-01
##  [389,] 0.436239133 0.2755194522 5.800410e-02
##  [390,] 0.392899701 0.1042386963 9.218388e-03
##  [391,] 0.406028666 0.1184250277 1.151354e-02
##  [392,] 0.349346279 0.3975319727 1.507880e-01
##  [393,] 0.017937464 0.2044870934 7.770510e-01
##  [394,] 0.340371253 0.0654560102 4.195898e-03
##  [395,] 0.340371253 0.0654560102 4.195898e-03
##  [396,] 0.406028666 0.1184250277 1.151354e-02
##  [397,] 0.321175019 0.4163379880 1.798991e-01
##  [398,] 0.438655970 0.1794501695 2.447048e-02
##  [399,] 0.430813836 0.2910904300 6.556091e-02
##  [400,] 0.349346279 0.3975319727 1.507880e-01
##  [401,] 0.444358195 0.2275981001 3.885821e-02
##  [402,] 0.227598100 0.4443581954 2.891855e-01
##  [403,] 0.204487093 0.0179374643 5.244873e-04
##  [404,] 0.443086838 0.2436977611 4.467792e-02
##  [405,] 0.266544426 0.0339238361 1.439193e-03
##  [406,] 0.397531973 0.3493462791 1.023338e-01
##  [407,] 0.335537578 0.4074384881 1.649156e-01
##  [408,] 0.417093250 0.1331148669 1.416116e-02
##  [409,] 0.442218287 0.1953987782 2.877966e-02
##  [410,] 0.426168977 0.1482326877 1.718640e-02
##  [411,] 0.349346279 0.3975319727 1.507880e-01
##  [412,] 0.362525595 0.3866939680 1.374912e-01
##  [413,] 0.148232688 0.4261689772 4.084119e-01
##  [414,] 0.306334128 0.4241549461 1.957638e-01
##  [415,] 0.362525595 0.3866939680 1.374912e-01
##  [416,] 0.406028666 0.1184250277 1.151354e-02
##  [417,] 0.442218287 0.1953987782 2.877966e-02
##  [418,] 0.046838810 0.0007678494 4.195898e-06
##  [419,] 0.436239133 0.2755194522 5.800410e-02
##  [420,] 0.293645732 0.0435030714 2.148300e-03
##  [421,] 0.407438488 0.3355375785 9.210835e-02
##  [422,] 0.000000000 0.0000000000 0.000000e+00
##  [423,] 0.430813836 0.2910904300 6.556091e-02
##  [424,] 0.179450170 0.4386559699 3.574234e-01
##  [425,] 0.443086838 0.2436977611 4.467792e-02
##  [426,] 0.406028666 0.1184250277 1.151354e-02
##  [427,] 0.386693968 0.3625255950 1.132892e-01
##  [428,] 0.433331375 0.1637029640 2.061445e-02
##  [429,] 0.397531973 0.3493462791 1.023338e-01
##  [430,] 0.291090430 0.4308138364 2.125348e-01
##  [431,] 0.335537578 0.4074384881 1.649156e-01
##  [432,] 0.318229499 0.0540389715 3.058810e-03
##  [433,] 0.169380014 0.0116813803 2.685375e-04
##  [434,] 0.436239133 0.2755194522 5.800410e-02
##  [435,] 0.360146521 0.0776786613 5.584740e-03
##  [436,] 0.392899701 0.1042386963 9.218388e-03
##  [437,] 0.227598100 0.4443581954 2.891855e-01
##  [438,] 0.438655970 0.1794501695 2.447048e-02
##  [439,] 0.406028666 0.1184250277 1.151354e-02
##  [440,] 0.406028666 0.1184250277 1.151354e-02
##  [441,] 0.266544426 0.0339238361 1.439193e-03
##  [442,] 0.430813836 0.2910904300 6.556091e-02
##  [443,] 0.259696720 0.4403553087 2.488965e-01
##  [444,] 0.375000000 0.3750000000 1.250000e-01
##  [445,] 0.440355309 0.2596967205 5.105149e-02
##  [446,] 0.211473264 0.4440938538 3.108657e-01
##  [447,] 0.275519452 0.4362391326 2.302373e-01
##  [448,] 0.318229499 0.0540389715 3.058810e-03
##  [449,] 0.397531973 0.3493462791 1.023338e-01
##  [450,] 0.440355309 0.2596967205 5.105149e-02
##  [451,] 0.360146521 0.0776786613 5.584740e-03
##  [452,] 0.436239133 0.2755194522 5.800410e-02
##  [453,] 0.349346279 0.3975319727 1.507880e-01
##  [454,] 0.397531973 0.3493462791 1.023338e-01
##  [455,] 0.392899701 0.1042386963 9.218388e-03
##  [456,] 0.227598100 0.4443581954 2.891855e-01
##  [457,] 0.436239133 0.2755194522 5.800410e-02
##  [458,] 0.433331375 0.1637029640 2.061445e-02
##  [459,] 0.444093854 0.2114732637 3.356718e-02
##  [460,] 0.416337988 0.3211750193 8.258786e-02
##  [461,] 0.243697761 0.4430868383 2.685375e-01
##  [462,] 0.293645732 0.0435030714 2.148300e-03
##  [463,] 0.377630828 0.0906313987 7.250512e-03
##  [464,] 0.444093854 0.2114732637 3.356718e-02
##  [465,] 0.335537578 0.4074384881 1.649156e-01
##  [466,] 0.321175019 0.4163379880 1.798991e-01
##  [467,] 0.335537578 0.4074384881 1.649156e-01
##  [468,] 0.318229499 0.0540389715 3.058810e-03
##  [469,] 0.406028666 0.1184250277 1.151354e-02
##  [470,] 0.430813836 0.2910904300 6.556091e-02
##  [471,] 0.362525595 0.3866939680 1.374912e-01
##  [472,] 0.321175019 0.4163379880 1.798991e-01
##  [473,] 0.306334128 0.4241549461 1.957638e-01
##  [474,] 0.236850055 0.0253767916 9.063140e-04
##  [475,] 0.443086838 0.2436977611 4.467792e-02
##  [476,] 0.377630828 0.0906313987 7.250512e-03
##  [477,] 0.291090430 0.4308138364 2.125348e-01
##  [478,] 0.416337988 0.3211750193 8.258786e-02
##  [479,] 0.424154946 0.3063341278 7.374710e-02
##  [480,] 0.442218287 0.1953987782 2.877966e-02
##  [481,] 0.424154946 0.3063341278 7.374710e-02
##  [482,] 0.335537578 0.4074384881 1.649156e-01
##  [483,] 0.291090430 0.4308138364 2.125348e-01
##  [484,] 0.430813836 0.2910904300 6.556091e-02
##  [485,] 0.318229499 0.0540389715 3.058810e-03
##  [486,] 0.430813836 0.2910904300 6.556091e-02
##  [487,] 0.377630828 0.0906313987 7.250512e-03
##  [488,] 0.430813836 0.2910904300 6.556091e-02
##  [489,] 0.386693968 0.3625255950 1.132892e-01
##  [490,] 0.417093250 0.1331148669 1.416116e-02
##  [491,] 0.362525595 0.3866939680 1.374912e-01
##  [492,] 0.375000000 0.3750000000 1.250000e-01
##  [493,] 0.236850055 0.0253767916 9.063140e-04
##  [494,] 0.424154946 0.3063341278 7.374710e-02
##  [495,] 0.417093250 0.1331148669 1.416116e-02
##  [496,] 0.386693968 0.3625255950 1.132892e-01
##  [497,] 0.275519452 0.4362391326 2.302373e-01
##  [498,] 0.424154946 0.3063341278 7.374710e-02
##  [499,] 0.318229499 0.0540389715 3.058810e-03
##  [500,] 0.243697761 0.4430868383 2.685375e-01
##  [501,] 0.335537578 0.4074384881 1.649156e-01
##  [502,] 0.349346279 0.3975319727 1.507880e-01
##  [503,] 0.392899701 0.1042386963 9.218388e-03
##  [504,] 0.416337988 0.3211750193 8.258786e-02
##  [505,] 0.430813836 0.2910904300 6.556091e-02
##  [506,] 0.407438488 0.3355375785 9.210835e-02
##  [507,] 0.349346279 0.3975319727 1.507880e-01
##  [508,] 0.335537578 0.4074384881 1.649156e-01
##  [509,] 0.443086838 0.2436977611 4.467792e-02
##  [510,] 0.293645732 0.0435030714 2.148300e-03
##  [511,] 0.375000000 0.3750000000 1.250000e-01
##  [512,] 0.444093854 0.2114732637 3.356718e-02
##  [513,] 0.362525595 0.3866939680 1.374912e-01
##  [514,] 0.163702964 0.4333313752 3.823512e-01
##  [515,] 0.433331375 0.1637029640 2.061445e-02
##  [516,] 0.417093250 0.1331148669 1.416116e-02
##  [517,] 0.360146521 0.0776786613 5.584740e-03
##  [518,] 0.179450170 0.4386559699 3.574234e-01
##  [519,] 0.243697761 0.4430868383 2.685375e-01
##  [520,] 0.444358195 0.2275981001 3.885821e-02
##  [521,] 0.236850055 0.0253767916 9.063140e-04
##  [522,] 0.195398778 0.4422182874 3.336033e-01
##  [523,] 0.243697761 0.4430868383 2.685375e-01
##  [524,] 0.397531973 0.3493462791 1.023338e-01
##  [525,] 0.444093854 0.2114732637 3.356718e-02
##  [526,] 0.392899701 0.1042386963 9.218388e-03
##  [527,] 0.275519452 0.4362391326 2.302373e-01
##  [528,] 0.424154946 0.3063341278 7.374710e-02
##  [529,] 0.392899701 0.1042386963 9.218388e-03
##  [530,] 0.291090430 0.4308138364 2.125348e-01
##  [531,] 0.362525595 0.3866939680 1.374912e-01
##  [532,] 0.266544426 0.0339238361 1.439193e-03
##  [533,] 0.291090430 0.4308138364 2.125348e-01
##  [534,] 0.340371253 0.0654560102 4.195898e-03
##  [535,] 0.377630828 0.0906313987 7.250512e-03
##  [536,] 0.407438488 0.3355375785 9.210835e-02
##  [537,] 0.204487093 0.0179374643 5.244873e-04
##  [538,] 0.211473264 0.4440938538 3.108657e-01
##  [539,] 0.416337988 0.3211750193 8.258786e-02
##  [540,] 0.417093250 0.1331148669 1.416116e-02
##  [541,] 0.243697761 0.4430868383 2.685375e-01
##  [542,] 0.236850055 0.0253767916 9.063140e-04
##  [543,] 0.275519452 0.4362391326 2.302373e-01
##  [544,] 0.275519452 0.4362391326 2.302373e-01
##  [545,] 0.275519452 0.4362391326 2.302373e-01
##  [546,] 0.416337988 0.3211750193 8.258786e-02
##  [547,] 0.243697761 0.4430868383 2.685375e-01
##  [548,] 0.377630828 0.0906313987 7.250512e-03
##  [549,] 0.407438488 0.3355375785 9.210835e-02
##  [550,] 0.386693968 0.3625255950 1.132892e-01
##  [551,] 0.392899701 0.1042386963 9.218388e-03
##  [552,] 0.306334128 0.4241549461 1.957638e-01
##  [553,] 0.335537578 0.4074384881 1.649156e-01
##  [554,] 0.065456010 0.3403712531 5.899768e-01
##  [555,] 0.424154946 0.3063341278 7.374710e-02
##  [556,] 0.426168977 0.1482326877 1.718640e-02
##  [557,] 0.340371253 0.0654560102 4.195898e-03
##  [558,] 0.444358195 0.2275981001 3.885821e-02
##  [559,] 0.335537578 0.4074384881 1.649156e-01
##  [560,] 0.426168977 0.1482326877 1.718640e-02
##  [561,] 0.417093250 0.1331148669 1.416116e-02
##  [562,] 0.416337988 0.3211750193 8.258786e-02
##  [563,] 0.243697761 0.4430868383 2.685375e-01
##  [564,] 0.163702964 0.4333313752 3.823512e-01
##  [565,] 0.321175019 0.4163379880 1.798991e-01
##  [566,] 0.131453291 0.0066840657 1.132892e-04
##  [567,] 0.444093854 0.2114732637 3.356718e-02
##  [568,] 0.000000000 0.0000000000 0.000000e+00
##  [569,] 0.340371253 0.0654560102 4.195898e-03
##  [570,] 0.417093250 0.1331148669 1.416116e-02
##  [571,] 0.406028666 0.1184250277 1.151354e-02
##  [572,] 0.340371253 0.0654560102 4.195898e-03
##  [573,] 0.397531973 0.3493462791 1.023338e-01
##  [574,] 0.321175019 0.4163379880 1.798991e-01
##  [575,] 0.386693968 0.3625255950 1.132892e-01
##  [576,] 0.438655970 0.1794501695 2.447048e-02
##  [577,] 0.090631399 0.3776308281 5.244873e-01
##  [578,] 0.133114867 0.4170932496 4.356307e-01
##  [579,] 0.443086838 0.2436977611 4.467792e-02
##  [580,] 0.438655970 0.1794501695 2.447048e-02
##  [581,] 0.442218287 0.1953987782 2.877966e-02
##  [582,] 0.236850055 0.0253767916 9.063140e-04
##  [583,] 0.118425028 0.4060286664 4.640328e-01
##  [584,] 0.417093250 0.1331148669 1.416116e-02
##  [585,] 0.424154946 0.3063341278 7.374710e-02
##  [586,] 0.386693968 0.3625255950 1.132892e-01
##  [587,] 0.397531973 0.3493462791 1.023338e-01
##  [588,] 0.440355309 0.2596967205 5.105149e-02
##  [589,] 0.291090430 0.4308138364 2.125348e-01
##  [590,] 0.417093250 0.1331148669 1.416116e-02
##  [591,] 0.275519452 0.4362391326 2.302373e-01
##  [592,] 0.360146521 0.0776786613 5.584740e-03
##  [593,] 0.397531973 0.3493462791 1.023338e-01
##  [594,] 0.416337988 0.3211750193 8.258786e-02
##  [595,] 0.266544426 0.0339238361 1.439193e-03
##  [596,] 0.416337988 0.3211750193 8.258786e-02
##  [597,] 0.443086838 0.2436977611 4.467792e-02
##  [598,] 0.275519452 0.4362391326 2.302373e-01
##  [599,] 0.444358195 0.2275981001 3.885821e-02
##  [600,] 0.291090430 0.4308138364 2.125348e-01
##  [601,] 0.195398778 0.4422182874 3.336033e-01
##  [602,] 0.444358195 0.2275981001 3.885821e-02
##  [603,] 0.377630828 0.0906313987 7.250512e-03
##  [604,] 0.417093250 0.1331148669 1.416116e-02
##  [605,] 0.433331375 0.1637029640 2.061445e-02
##  [606,] 0.442218287 0.1953987782 2.877966e-02
##  [607,] 0.417093250 0.1331148669 1.416116e-02
##  [608,] 0.386693968 0.3625255950 1.132892e-01
##  [609,] 0.397531973 0.3493462791 1.023338e-01
##  [610,] 0.211473264 0.4440938538 3.108657e-01
##  [611,] 0.340371253 0.0654560102 4.195898e-03
##  [612,] 0.340371253 0.0654560102 4.195898e-03
##  [613,] 0.386693968 0.3625255950 1.132892e-01
##  [614,] 0.360146521 0.0776786613 5.584740e-03
##  [615,] 0.443086838 0.2436977611 4.467792e-02
##  [616,] 0.406028666 0.1184250277 1.151354e-02
##  [617,] 0.443086838 0.2436977611 4.467792e-02
##  [618,] 0.436239133 0.2755194522 5.800410e-02
##  [619,] 0.438655970 0.1794501695 2.447048e-02
##  [620,] 0.444358195 0.2275981001 3.885821e-02
##  [621,] 0.424154946 0.3063341278 7.374710e-02
##  [622,] 0.430813836 0.2910904300 6.556091e-02
##  [623,] 0.424154946 0.3063341278 7.374710e-02
##  [624,] 0.360146521 0.0776786613 5.584740e-03
##  [625,] 0.375000000 0.3750000000 1.250000e-01
##  [626,] 0.407438488 0.3355375785 9.210835e-02
##  [627,] 0.440355309 0.2596967205 5.105149e-02
##  [628,] 0.335537578 0.4074384881 1.649156e-01
##  [629,] 0.430813836 0.2910904300 6.556091e-02
##  [630,] 0.444093854 0.2114732637 3.356718e-02
##  [631,] 0.436239133 0.2755194522 5.800410e-02
##  [632,] 0.275519452 0.4362391326 2.302373e-01
##  [633,] 0.444358195 0.2275981001 3.885821e-02
##  [634,] 0.417093250 0.1331148669 1.416116e-02
##  [635,] 0.417093250 0.1331148669 1.416116e-02
##  [636,] 0.440355309 0.2596967205 5.105149e-02
##  [637,] 0.424154946 0.3063341278 7.374710e-02
##  [638,] 0.416337988 0.3211750193 8.258786e-02
##  [639,] 0.360146521 0.0776786613 5.584740e-03
##  [640,] 0.436239133 0.2755194522 5.800410e-02
##  [641,] 0.090631399 0.3776308281 5.244873e-01
##  [642,] 0.397531973 0.3493462791 1.023338e-01
##  [643,] 0.377630828 0.0906313987 7.250512e-03
##  [644,] 0.375000000 0.3750000000 1.250000e-01
##  [645,] 0.438655970 0.1794501695 2.447048e-02
##  [646,] 0.424154946 0.3063341278 7.374710e-02
##  [647,] 0.306334128 0.4241549461 1.957638e-01
##  [648,] 0.436239133 0.2755194522 5.800410e-02
##  [649,] 0.444358195 0.2275981001 3.885821e-02
##  [650,] 0.377630828 0.0906313987 7.250512e-03
##  [651,] 0.417093250 0.1331148669 1.416116e-02
##  [652,] 0.340371253 0.0654560102 4.195898e-03
##  [653,] 0.444093854 0.2114732637 3.356718e-02
##  [654,] 0.377630828 0.0906313987 7.250512e-03
##  [655,] 0.266544426 0.0339238361 1.439193e-03
##  [656,] 0.293645732 0.0435030714 2.148300e-03
##  [657,] 0.179450170 0.4386559699 3.574234e-01
##  [658,] 0.406028666 0.1184250277 1.151354e-02
##  [659,] 0.443086838 0.2436977611 4.467792e-02
##  [660,] 0.375000000 0.3750000000 1.250000e-01
##  [661,] 0.407438488 0.3355375785 9.210835e-02
##  [662,] 0.436239133 0.2755194522 5.800410e-02
##  [663,] 0.243697761 0.4430868383 2.685375e-01
##  [664,] 0.377630828 0.0906313987 7.250512e-03
##  [665,] 0.318229499 0.0540389715 3.058810e-03
##  [666,] 0.291090430 0.4308138364 2.125348e-01
##  [667,] 0.362525595 0.3866939680 1.374912e-01
##  [668,] 0.291090430 0.4308138364 2.125348e-01
##  [669,] 0.443086838 0.2436977611 4.467792e-02
##  [670,] 0.406028666 0.1184250277 1.151354e-02
##  [671,] 0.318229499 0.0540389715 3.058810e-03
##  [672,] 0.375000000 0.3750000000 1.250000e-01
##  [673,] 0.362525595 0.3866939680 1.374912e-01
##  [674,] 0.259696720 0.4403553087 2.488965e-01
##  [675,] 0.043503071 0.2936457319 6.607029e-01
##  [676,] 0.438655970 0.1794501695 2.447048e-02
##  [677,] 0.163702964 0.4333313752 3.823512e-01
##  [678,] 0.407438488 0.3355375785 9.210835e-02
##  [679,] 0.291090430 0.4308138364 2.125348e-01
##  [680,] 0.424154946 0.3063341278 7.374710e-02
##  [681,] 0.424154946 0.3063341278 7.374710e-02
##  [682,] 0.406028666 0.1184250277 1.151354e-02
##  [683,] 0.211473264 0.4440938538 3.108657e-01
##  [684,] 0.436239133 0.2755194522 5.800410e-02
##  [685,] 0.392899701 0.1042386963 9.218388e-03
##  [686,] 0.306334128 0.4241549461 1.957638e-01
##  [687,] 0.407438488 0.3355375785 9.210835e-02
##  [688,] 0.362525595 0.3866939680 1.374912e-01
##  [689,] 0.417093250 0.1331148669 1.416116e-02
##  [690,] 0.426168977 0.1482326877 1.718640e-02
##  [691,] 0.349346279 0.3975319727 1.507880e-01
##  [692,] 0.417093250 0.1331148669 1.416116e-02
##  [693,] 0.227598100 0.4443581954 2.891855e-01
##  [694,] 0.340371253 0.0654560102 4.195898e-03
##  [695,] 0.443086838 0.2436977611 4.467792e-02
##  [696,] 0.360146521 0.0776786613 5.584740e-03
##  [697,] 0.426168977 0.1482326877 1.718640e-02
##  [698,] 0.266544426 0.0339238361 1.439193e-03
##  [699,] 0.118425028 0.4060286664 4.640328e-01
##  [700,] 0.430813836 0.2910904300 6.556091e-02
##  [701,] 0.416337988 0.3211750193 8.258786e-02
##  [702,] 0.433331375 0.1637029640 2.061445e-02
##  [703,] 0.430813836 0.2910904300 6.556091e-02
##  [704,] 0.375000000 0.3750000000 1.250000e-01
##  [705,] 0.211473264 0.4440938538 3.108657e-01
##  [706,] 0.291090430 0.4308138364 2.125348e-01
##  [707,] 0.406028666 0.1184250277 1.151354e-02
##  [708,] 0.321175019 0.4163379880 1.798991e-01
##  [709,] 0.259696720 0.4403553087 2.488965e-01
##  [710,] 0.227598100 0.4443581954 2.891855e-01
##  [711,] 0.275519452 0.4362391326 2.302373e-01
##  [712,] 0.211473264 0.4440938538 3.108657e-01
##  [713,] 0.386693968 0.3625255950 1.132892e-01
##  [714,] 0.444358195 0.2275981001 3.885821e-02
##  [715,] 0.406028666 0.1184250277 1.151354e-02
##  [716,] 0.349346279 0.3975319727 1.507880e-01
##  [717,] 0.397531973 0.3493462791 1.023338e-01
##  [718,] 0.424154946 0.3063341278 7.374710e-02
##  [719,] 0.407438488 0.3355375785 9.210835e-02
##  [720,] 0.236850055 0.0253767916 9.063140e-04
##  [721,] 0.442218287 0.1953987782 2.877966e-02
##  [722,] 0.392899701 0.1042386963 9.218388e-03
##  [723,] 0.043503071 0.2936457319 6.607029e-01
##  [724,] 0.362525595 0.3866939680 1.374912e-01
##  [725,] 0.318229499 0.0540389715 3.058810e-03
##  [726,] 0.318229499 0.0540389715 3.058810e-03
##  [727,] 0.440355309 0.2596967205 5.105149e-02
##  [728,] 0.090631399 0.0030210466 3.356718e-05
##  [729,] 0.266544426 0.0339238361 1.439193e-03
##  [730,] 0.440355309 0.2596967205 5.105149e-02
##  [731,] 0.321175019 0.4163379880 1.798991e-01
##  [732,] 0.416337988 0.3211750193 8.258786e-02
##  [733,] 0.406028666 0.1184250277 1.151354e-02
##  [734,] 0.397531973 0.3493462791 1.023338e-01
##  [735,] 0.293645732 0.0435030714 2.148300e-03
##  [736,] 0.406028666 0.1184250277 1.151354e-02
##  [737,] 0.407438488 0.3355375785 9.210835e-02
##  [738,] 0.397531973 0.3493462791 1.023338e-01
##  [739,] 0.291090430 0.4308138364 2.125348e-01
##  [740,] 0.375000000 0.3750000000 1.250000e-01
##  [741,] 0.266544426 0.0339238361 1.439193e-03
##  [742,] 0.211473264 0.4440938538 3.108657e-01
##  [743,] 0.179450170 0.4386559699 3.574234e-01
##  [744,] 0.163702964 0.4333313752 3.823512e-01
##  [745,] 0.360146521 0.0776786613 5.584740e-03
##  [746,] 0.349346279 0.3975319727 1.507880e-01
##  [747,] 0.340371253 0.0654560102 4.195898e-03
##  [748,] 0.438655970 0.1794501695 2.447048e-02
##  [749,] 0.340371253 0.0654560102 4.195898e-03
##  [750,] 0.444093854 0.2114732637 3.356718e-02
##  [751,] 0.433331375 0.1637029640 2.061445e-02
##  [752,] 0.440355309 0.2596967205 5.105149e-02
##  [753,] 0.227598100 0.4443581954 2.891855e-01
##  [754,] 0.349346279 0.3975319727 1.507880e-01
##  [755,] 0.426168977 0.1482326877 1.718640e-02
##  [756,] 0.406028666 0.1184250277 1.151354e-02
##  [757,] 0.362525595 0.3866939680 1.374912e-01
##  [758,] 0.266544426 0.0339238361 1.439193e-03
##  [759,] 0.430813836 0.2910904300 6.556091e-02
##  [760,] 0.362525595 0.3866939680 1.374912e-01
##  [761,] 0.444358195 0.2275981001 3.885821e-02
##  [762,] 0.406028666 0.1184250277 1.151354e-02
##  [763,] 0.163702964 0.4333313752 3.823512e-01
##  [764,] 0.104238696 0.3928997013 4.936432e-01
##  [765,] 0.444358195 0.2275981001 3.885821e-02
##  [766,] 0.397531973 0.3493462791 1.023338e-01
##  [767,] 0.195398778 0.4422182874 3.336033e-01
##  [768,] 0.195398778 0.4422182874 3.336033e-01
##  [769,] 0.131453291 0.0066840657 1.132892e-04
##  [770,] 0.397531973 0.3493462791 1.023338e-01
##  [771,] 0.438655970 0.1794501695 2.447048e-02
##  [772,] 0.438655970 0.1794501695 2.447048e-02
##  [773,] 0.436239133 0.2755194522 5.800410e-02
##  [774,] 0.306334128 0.4241549461 1.957638e-01
##  [775,] 0.318229499 0.0540389715 3.058810e-03
##  [776,] 0.438655970 0.1794501695 2.447048e-02
##  [777,] 0.433331375 0.1637029640 2.061445e-02
##  [778,] 0.436239133 0.2755194522 5.800410e-02
##  [779,] 0.440355309 0.2596967205 5.105149e-02
##  [780,] 0.433331375 0.1637029640 2.061445e-02
##  [781,] 0.426168977 0.1482326877 1.718640e-02
##  [782,] 0.406028666 0.1184250277 1.151354e-02
##  [783,] 0.375000000 0.3750000000 1.250000e-01
##  [784,] 0.377630828 0.0906313987 7.250512e-03
##  [785,] 0.417093250 0.1331148669 1.416116e-02
##  [786,] 0.442218287 0.1953987782 2.877966e-02
##  [787,] 0.407438488 0.3355375785 9.210835e-02
##  [788,] 0.163702964 0.4333313752 3.823512e-01
##  [789,] 0.440355309 0.2596967205 5.105149e-02
##  [790,] 0.443086838 0.2436977611 4.467792e-02
##  [791,] 0.416337988 0.3211750193 8.258786e-02
##  [792,] 0.386693968 0.3625255950 1.132892e-01
##  [793,] 0.340371253 0.0654560102 4.195898e-03
##  [794,] 0.133114867 0.4170932496 4.356307e-01
##  [795,] 0.386693968 0.3625255950 1.132892e-01
##  [796,] 0.377630828 0.0906313987 7.250512e-03
##  [797,] 0.442218287 0.1953987782 2.877966e-02
##  [798,] 0.433331375 0.1637029640 2.061445e-02
##  [799,] 0.417093250 0.1331148669 1.416116e-02
##  [800,] 0.440355309 0.2596967205 5.105149e-02
##  [801,] 0.426168977 0.1482326877 1.718640e-02
##  [802,] 0.375000000 0.3750000000 1.250000e-01
##  [803,] 0.179450170 0.4386559699 3.574234e-01
##  [804,] 0.392899701 0.1042386963 9.218388e-03
##  [805,] 0.430813836 0.2910904300 6.556091e-02
##  [806,] 0.386693968 0.3625255950 1.132892e-01
##  [807,] 0.362525595 0.3866939680 1.374912e-01
##  [808,] 0.335537578 0.4074384881 1.649156e-01
##  [809,] 0.407438488 0.3355375785 9.210835e-02
##  [810,] 0.443086838 0.2436977611 4.467792e-02
##  [811,] 0.430813836 0.2910904300 6.556091e-02
##  [812,] 0.306334128 0.4241549461 1.957638e-01
##  [813,] 0.406028666 0.1184250277 1.151354e-02
##  [814,] 0.340371253 0.0654560102 4.195898e-03
##  [815,] 0.417093250 0.1331148669 1.416116e-02
##  [816,] 0.440355309 0.2596967205 5.105149e-02
##  [817,] 0.392899701 0.1042386963 9.218388e-03
##  [818,] 0.386693968 0.3625255950 1.132892e-01
##  [819,] 0.362525595 0.3866939680 1.374912e-01
##  [820,] 0.397531973 0.3493462791 1.023338e-01
##  [821,] 0.443086838 0.2436977611 4.467792e-02
##  [822,] 0.306334128 0.4241549461 1.957638e-01
##  [823,] 0.236850055 0.0253767916 9.063140e-04
##  [824,] 0.426168977 0.1482326877 1.718640e-02
##  [825,] 0.377630828 0.0906313987 7.250512e-03
##  [826,] 0.433331375 0.1637029640 2.061445e-02
##  [827,] 0.054038972 0.3182294988 6.246727e-01
##  [828,] 0.444358195 0.2275981001 3.885821e-02
##  [829,] 0.417093250 0.1331148669 1.416116e-02
##  [830,] 0.011681380 0.1693800141 8.186701e-01
##  [831,] 0.426168977 0.1482326877 1.718640e-02
##  [832,] 0.293645732 0.0435030714 2.148300e-03
##  [833,] 0.349346279 0.3975319727 1.507880e-01
##  [834,] 0.266544426 0.0339238361 1.439193e-03
##  [835,] 0.179450170 0.4386559699 3.574234e-01
##  [836,] 0.442218287 0.1953987782 2.877966e-02
##  [837,] 0.406028666 0.1184250277 1.151354e-02
##  [838,] 0.438655970 0.1794501695 2.447048e-02
##  [839,] 0.444358195 0.2275981001 3.885821e-02
##  [840,] 0.407438488 0.3355375785 9.210835e-02
##  [841,] 0.386693968 0.3625255950 1.132892e-01
##  [842,] 0.362525595 0.3866939680 1.374912e-01
##  [843,] 0.386693968 0.3625255950 1.132892e-01
##  [844,] 0.397531973 0.3493462791 1.023338e-01
##  [845,] 0.090631399 0.0030210466 3.356718e-05
##  [846,] 0.211473264 0.4440938538 3.108657e-01
##  [847,] 0.442218287 0.1953987782 2.877966e-02
##  [848,] 0.306334128 0.4241549461 1.957638e-01
##  [849,] 0.349346279 0.3975319727 1.507880e-01
##  [850,] 0.433331375 0.1637029640 2.061445e-02
##  [851,] 0.444093854 0.2114732637 3.356718e-02
##  [852,] 0.179450170 0.4386559699 3.574234e-01
##  [853,] 0.397531973 0.3493462791 1.023338e-01
##  [854,] 0.340371253 0.0654560102 4.195898e-03
##  [855,] 0.195398778 0.4422182874 3.336033e-01
##  [856,] 0.293645732 0.0435030714 2.148300e-03
##  [857,] 0.340371253 0.0654560102 4.195898e-03
##  [858,] 0.436239133 0.2755194522 5.800410e-02
##  [859,] 0.362525595 0.3866939680 1.374912e-01
##  [860,] 0.407438488 0.3355375785 9.210835e-02
##  [861,] 0.443086838 0.2436977611 4.467792e-02
##  [862,] 0.444093854 0.2114732637 3.356718e-02
##  [863,] 0.430813836 0.2910904300 6.556091e-02
##  [864,] 0.430813836 0.2910904300 6.556091e-02
##  [865,] 0.243697761 0.4430868383 2.685375e-01
##  [866,] 0.211473264 0.4440938538 3.108657e-01
##  [867,] 0.416337988 0.3211750193 8.258786e-02
##  [868,] 0.397531973 0.3493462791 1.023338e-01
##  [869,] 0.227598100 0.4443581954 2.891855e-01
##  [870,] 0.438655970 0.1794501695 2.447048e-02
##  [871,] 0.443086838 0.2436977611 4.467792e-02
##  [872,] 0.436239133 0.2755194522 5.800410e-02
##  [873,] 0.444093854 0.2114732637 3.356718e-02
##  [874,] 0.243697761 0.4430868383 2.685375e-01
##  [875,] 0.433331375 0.1637029640 2.061445e-02
##  [876,] 0.377630828 0.0906313987 7.250512e-03
##  [877,] 0.443086838 0.2436977611 4.467792e-02
##  [878,] 0.426168977 0.1482326877 1.718640e-02
##  [879,] 0.306334128 0.4241549461 1.957638e-01
##  [880,] 0.362525595 0.3866939680 1.374912e-01
##  [881,] 0.436239133 0.2755194522 5.800410e-02
##  [882,] 0.416337988 0.3211750193 8.258786e-02
##  [883,] 0.227598100 0.4443581954 2.891855e-01
##  [884,] 0.424154946 0.3063341278 7.374710e-02
##  [885,] 0.293645732 0.0435030714 2.148300e-03
##  [886,] 0.443086838 0.2436977611 4.467792e-02
##  [887,] 0.169380014 0.0116813803 2.685375e-04
##  [888,] 0.430813836 0.2910904300 6.556091e-02
##  [889,] 0.424154946 0.3063341278 7.374710e-02
##  [890,] 0.321175019 0.4163379880 1.798991e-01
##  [891,] 0.306334128 0.4241549461 1.957638e-01
##  [892,] 0.291090430 0.4308138364 2.125348e-01
##  [893,] 0.386693968 0.3625255950 1.132892e-01
##  [894,] 0.444093854 0.2114732637 3.356718e-02
##  [895,] 0.266544426 0.0339238361 1.439193e-03
##  [896,] 0.227598100 0.4443581954 2.891855e-01
##  [897,] 0.444093854 0.2114732637 3.356718e-02
##  [898,] 0.443086838 0.2436977611 4.467792e-02
##  [899,] 0.211473264 0.4440938538 3.108657e-01
##  [900,] 0.426168977 0.1482326877 1.718640e-02
##  [901,] 0.444358195 0.2275981001 3.885821e-02
##  [902,] 0.293645732 0.0435030714 2.148300e-03
##  [903,] 0.340371253 0.0654560102 4.195898e-03
##  [904,] 0.318229499 0.0540389715 3.058810e-03
##  [905,] 0.426168977 0.1482326877 1.718640e-02
##  [906,] 0.444093854 0.2114732637 3.356718e-02
##  [907,] 0.243697761 0.4430868383 2.685375e-01
##  [908,] 0.436239133 0.2755194522 5.800410e-02
##  [909,] 0.406028666 0.1184250277 1.151354e-02
##  [910,] 0.318229499 0.0540389715 3.058810e-03
##  [911,] 0.362525595 0.3866939680 1.374912e-01
##  [912,] 0.266544426 0.0339238361 1.439193e-03
##  [913,] 0.211473264 0.4440938538 3.108657e-01
##  [914,] 0.179450170 0.4386559699 3.574234e-01
##  [915,] 0.444358195 0.2275981001 3.885821e-02
##  [916,] 0.204487093 0.0179374643 5.244873e-04
##  [917,] 0.397531973 0.3493462791 1.023338e-01
##  [918,] 0.406028666 0.1184250277 1.151354e-02
##  [919,] 0.259696720 0.4403553087 2.488965e-01
##  [920,] 0.443086838 0.2436977611 4.467792e-02
##  [921,] 0.259696720 0.4403553087 2.488965e-01
##  [922,] 0.340371253 0.0654560102 4.195898e-03
##  [923,] 0.243697761 0.4430868383 2.685375e-01
##  [924,] 0.440355309 0.2596967205 5.105149e-02
##  [925,] 0.321175019 0.4163379880 1.798991e-01
##  [926,] 0.318229499 0.0540389715 3.058810e-03
##  [927,] 0.046838810 0.0007678494 4.195898e-06
##  [928,] 0.204487093 0.0179374643 5.244873e-04
##  [929,] 0.392899701 0.1042386963 9.218388e-03
##  [930,] 0.436239133 0.2755194522 5.800410e-02
##  [931,] 0.335537578 0.4074384881 1.649156e-01
##  [932,] 0.090631399 0.0030210466 3.356718e-05
##  [933,] 0.293645732 0.0435030714 2.148300e-03
##  [934,] 0.443086838 0.2436977611 4.467792e-02
##  [935,] 0.360146521 0.0776786613 5.584740e-03
##  [936,] 0.442218287 0.1953987782 2.877966e-02
##  [937,] 0.442218287 0.1953987782 2.877966e-02
##  [938,] 0.169380014 0.0116813803 2.685375e-04
##  [939,] 0.436239133 0.2755194522 5.800410e-02
##  [940,] 0.424154946 0.3063341278 7.374710e-02
##  [941,] 0.416337988 0.3211750193 8.258786e-02
##  [942,] 0.436239133 0.2755194522 5.800410e-02
##  [943,] 0.335537578 0.4074384881 1.649156e-01
##  [944,] 0.407438488 0.3355375785 9.210835e-02
##  [945,] 0.227598100 0.4443581954 2.891855e-01
##  [946,] 0.335537578 0.4074384881 1.649156e-01
##  [947,] 0.148232688 0.4261689772 4.084119e-01
##  [948,] 0.416337988 0.3211750193 8.258786e-02
##  [949,] 0.321175019 0.4163379880 1.798991e-01
##  [950,] 0.340371253 0.0654560102 4.195898e-03
##  [951,] 0.335537578 0.4074384881 1.649156e-01
##  [952,] 0.440355309 0.2596967205 5.105149e-02
##  [953,] 0.424154946 0.3063341278 7.374710e-02
##  [954,] 0.386693968 0.3625255950 1.132892e-01
##  [955,] 0.397531973 0.3493462791 1.023338e-01
##  [956,] 0.392899701 0.1042386963 9.218388e-03
##  [957,] 0.340371253 0.0654560102 4.195898e-03
##  [958,] 0.416337988 0.3211750193 8.258786e-02
##  [959,] 0.275519452 0.4362391326 2.302373e-01
##  [960,] 0.397531973 0.3493462791 1.023338e-01
##  [961,] 0.440355309 0.2596967205 5.105149e-02
##  [962,] 0.340371253 0.0654560102 4.195898e-03
##  [963,] 0.386693968 0.3625255950 1.132892e-01
##  [964,] 0.397531973 0.3493462791 1.023338e-01
##  [965,] 0.259696720 0.4403553087 2.488965e-01
##  [966,] 0.444358195 0.2275981001 3.885821e-02
##  [967,] 0.416337988 0.3211750193 8.258786e-02
##  [968,] 0.335537578 0.4074384881 1.649156e-01
##  [969,] 0.443086838 0.2436977611 4.467792e-02
##  [970,] 0.386693968 0.3625255950 1.132892e-01
##  [971,] 0.416337988 0.3211750193 8.258786e-02
##  [972,] 0.259696720 0.4403553087 2.488965e-01
##  [973,] 0.006684066 0.1314532913 8.617494e-01
##  [974,] 0.386693968 0.3625255950 1.132892e-01
##  [975,] 0.275519452 0.4362391326 2.302373e-01
##  [976,] 0.444358195 0.2275981001 3.885821e-02
##  [977,] 0.375000000 0.3750000000 1.250000e-01
##  [978,] 0.243697761 0.4430868383 2.685375e-01
##  [979,] 0.407438488 0.3355375785 9.210835e-02
##  [980,] 0.444358195 0.2275981001 3.885821e-02
##  [981,] 0.293645732 0.0435030714 2.148300e-03
##  [982,] 0.397531973 0.3493462791 1.023338e-01
##  [983,] 0.443086838 0.2436977611 4.467792e-02
##  [984,] 0.195398778 0.4422182874 3.336033e-01
##  [985,] 0.444093854 0.2114732637 3.356718e-02
##  [986,] 0.000000000 0.0000000000 0.000000e+00
##  [987,] 0.318229499 0.0540389715 3.058810e-03
##  [988,] 0.360146521 0.0776786613 5.584740e-03
##  [989,] 0.362525595 0.3866939680 1.374912e-01
##  [990,] 0.266544426 0.0339238361 1.439193e-03
##  [991,] 0.433331375 0.1637029640 2.061445e-02
##  [992,] 0.440355309 0.2596967205 5.105149e-02
##  [993,] 0.444093854 0.2114732637 3.356718e-02
##  [994,] 0.375000000 0.3750000000 1.250000e-01
##  [995,] 0.438655970 0.1794501695 2.447048e-02
##  [996,] 0.118425028 0.4060286664 4.640328e-01
##  [997,] 0.340371253 0.0654560102 4.195898e-03
##  [998,] 0.436239133 0.2755194522 5.800410e-02
##  [999,] 0.090631399 0.0030210466 3.356718e-05
## [1000,] 0.442218287 0.1953987782 2.877966e-02
## [1001,] 0.243697761 0.4430868383 2.685375e-01
## [1002,] 0.416337988 0.3211750193 8.258786e-02
## [1003,] 0.148232688 0.4261689772 4.084119e-01
## [1004,] 0.416337988 0.3211750193 8.258786e-02
## [1005,] 0.335537578 0.4074384881 1.649156e-01
## [1006,] 0.436239133 0.2755194522 5.800410e-02
## [1007,] 0.443086838 0.2436977611 4.467792e-02
## [1008,] 0.407438488 0.3355375785 9.210835e-02
## [1009,] 0.291090430 0.4308138364 2.125348e-01
## [1010,] 0.321175019 0.4163379880 1.798991e-01
## [1011,] 0.416337988 0.3211750193 8.258786e-02
## [1012,] 0.406028666 0.1184250277 1.151354e-02
## [1013,] 0.436239133 0.2755194522 5.800410e-02
## [1014,] 0.433331375 0.1637029640 2.061445e-02
## [1015,] 0.444093854 0.2114732637 3.356718e-02
## [1016,] 0.392899701 0.1042386963 9.218388e-03
## [1017,] 0.440355309 0.2596967205 5.105149e-02
## [1018,] 0.416337988 0.3211750193 8.258786e-02
## [1019,] 0.362525595 0.3866939680 1.374912e-01
## [1020,] 0.360146521 0.0776786613 5.584740e-03
## [1021,] 0.406028666 0.1184250277 1.151354e-02
## [1022,] 0.349346279 0.3975319727 1.507880e-01
## [1023,] 0.360146521 0.0776786613 5.584740e-03
## [1024,] 0.406028666 0.1184250277 1.151354e-02
## [1025,] 0.392899701 0.1042386963 9.218388e-03
## [1026,] 0.360146521 0.0776786613 5.584740e-03
## [1027,] 0.340371253 0.0654560102 4.195898e-03
## [1028,] 0.362525595 0.3866939680 1.374912e-01
## [1029,] 0.375000000 0.3750000000 1.250000e-01
## [1030,] 0.293645732 0.0435030714 2.148300e-03
## [1031,] 0.392899701 0.1042386963 9.218388e-03
## [1032,] 0.179450170 0.4386559699 3.574234e-01
## [1033,] 0.433331375 0.1637029640 2.061445e-02
## [1034,] 0.291090430 0.4308138364 2.125348e-01
## [1035,] 0.430813836 0.2910904300 6.556091e-02
## [1036,] 0.243697761 0.4430868383 2.685375e-01
## [1037,] 0.444093854 0.2114732637 3.356718e-02
## [1038,] 0.375000000 0.3750000000 1.250000e-01
## [1039,] 0.179450170 0.4386559699 3.574234e-01
## [1040,] 0.293645732 0.0435030714 2.148300e-03
## [1041,] 0.407438488 0.3355375785 9.210835e-02
## [1042,] 0.243697761 0.4430868383 2.685375e-01
## [1043,] 0.163702964 0.4333313752 3.823512e-01
## [1044,] 0.104238696 0.3928997013 4.936432e-01
## [1045,] 0.349346279 0.3975319727 1.507880e-01
## [1046,] 0.407438488 0.3355375785 9.210835e-02
## [1047,] 0.443086838 0.2436977611 4.467792e-02
## [1048,] 0.131453291 0.0066840657 1.132892e-04
## [1049,] 0.349346279 0.3975319727 1.507880e-01
## [1050,] 0.430813836 0.2910904300 6.556091e-02
## [1051,] 0.416337988 0.3211750193 8.258786e-02
## [1052,] 0.417093250 0.1331148669 1.416116e-02
## [1053,] 0.444093854 0.2114732637 3.356718e-02
## [1054,] 0.424154946 0.3063341278 7.374710e-02
## [1055,] 0.362525595 0.3866939680 1.374912e-01
## [1056,] 0.291090430 0.4308138364 2.125348e-01
## [1057,] 0.375000000 0.3750000000 1.250000e-01
## [1058,] 0.443086838 0.2436977611 4.467792e-02
## [1059,] 0.131453291 0.0066840657 1.132892e-04
## [1060,] 0.211473264 0.4440938538 3.108657e-01
## [1061,] 0.195398778 0.4422182874 3.336033e-01
## [1062,] 0.424154946 0.3063341278 7.374710e-02
## [1063,] 0.430813836 0.2910904300 6.556091e-02
## [1064,] 0.360146521 0.0776786613 5.584740e-03
## [1065,] 0.293645732 0.0435030714 2.148300e-03
## [1066,] 0.340371253 0.0654560102 4.195898e-03
## [1067,] 0.444093854 0.2114732637 3.356718e-02
## [1068,] 0.416337988 0.3211750193 8.258786e-02
## [1069,] 0.444358195 0.2275981001 3.885821e-02
## [1070,] 0.424154946 0.3063341278 7.374710e-02
## [1071,] 0.416337988 0.3211750193 8.258786e-02
## [1072,] 0.275519452 0.4362391326 2.302373e-01
## [1073,] 0.443086838 0.2436977611 4.467792e-02
## [1074,] 0.054038972 0.3182294988 6.246727e-01
## [1075,] 0.377630828 0.0906313987 7.250512e-03
## [1076,] 0.416337988 0.3211750193 8.258786e-02
## [1077,] 0.440355309 0.2596967205 5.105149e-02
## [1078,] 0.443086838 0.2436977611 4.467792e-02
## [1079,] 0.407438488 0.3355375785 9.210835e-02
## [1080,] 0.444093854 0.2114732637 3.356718e-02
## [1081,] 0.293645732 0.0435030714 2.148300e-03
## [1082,] 0.407438488 0.3355375785 9.210835e-02
## [1083,] 0.436239133 0.2755194522 5.800410e-02
## [1084,] 0.426168977 0.1482326877 1.718640e-02
## [1085,] 0.407438488 0.3355375785 9.210835e-02
## [1086,] 0.442218287 0.1953987782 2.877966e-02
## [1087,] 0.335537578 0.4074384881 1.649156e-01
## [1088,] 0.430813836 0.2910904300 6.556091e-02
## [1089,] 0.335537578 0.4074384881 1.649156e-01
## [1090,] 0.397531973 0.3493462791 1.023338e-01
## [1091,] 0.444093854 0.2114732637 3.356718e-02
## [1092,] 0.321175019 0.4163379880 1.798991e-01
## [1093,] 0.433331375 0.1637029640 2.061445e-02
## [1094,] 0.444358195 0.2275981001 3.885821e-02
## [1095,] 0.416337988 0.3211750193 8.258786e-02
## [1096,] 0.195398778 0.4422182874 3.336033e-01
## [1097,] 0.148232688 0.4261689772 4.084119e-01
## [1098,] 0.444358195 0.2275981001 3.885821e-02
## [1099,] 0.407438488 0.3355375785 9.210835e-02
## [1100,] 0.266544426 0.0339238361 1.439193e-03
## [1101,] 0.243697761 0.4430868383 2.685375e-01
## [1102,] 0.335537578 0.4074384881 1.649156e-01
## [1103,] 0.416337988 0.3211750193 8.258786e-02
## [1104,] 0.440355309 0.2596967205 5.105149e-02
## [1105,] 0.436239133 0.2755194522 5.800410e-02
## [1106,] 0.392899701 0.1042386963 9.218388e-03
## [1107,] 0.397531973 0.3493462791 1.023338e-01
## [1108,] 0.444358195 0.2275981001 3.885821e-02
## [1109,] 0.321175019 0.4163379880 1.798991e-01
## [1110,] 0.440355309 0.2596967205 5.105149e-02
## [1111,] 0.163702964 0.4333313752 3.823512e-01
## [1112,] 0.204487093 0.0179374643 5.244873e-04
## [1113,] 0.179450170 0.4386559699 3.574234e-01
## [1114,] 0.430813836 0.2910904300 6.556091e-02
## [1115,] 0.360146521 0.0776786613 5.584740e-03
## [1116,] 0.426168977 0.1482326877 1.718640e-02
## [1117,] 0.444093854 0.2114732637 3.356718e-02
## [1118,] 0.266544426 0.0339238361 1.439193e-03
## [1119,] 0.375000000 0.3750000000 1.250000e-01
## [1120,] 0.407438488 0.3355375785 9.210835e-02
## [1121,] 0.377630828 0.0906313987 7.250512e-03
## [1122,] 0.417093250 0.1331148669 1.416116e-02
## [1123,] 0.360146521 0.0776786613 5.584740e-03
## [1124,] 0.406028666 0.1184250277 1.151354e-02
## [1125,] 0.306334128 0.4241549461 1.957638e-01
## [1126,] 0.443086838 0.2436977611 4.467792e-02
## [1127,] 0.377630828 0.0906313987 7.250512e-03
## [1128,] 0.375000000 0.3750000000 1.250000e-01
## [1129,] 0.266544426 0.0339238361 1.439193e-03
## [1130,] 0.424154946 0.3063341278 7.374710e-02
## [1131,] 0.440355309 0.2596967205 5.105149e-02
## [1132,] 0.306334128 0.4241549461 1.957638e-01
## [1133,] 0.266544426 0.0339238361 1.439193e-03
## [1134,] 0.163702964 0.4333313752 3.823512e-01
## [1135,] 0.375000000 0.3750000000 1.250000e-01
## [1136,] 0.236850055 0.0253767916 9.063140e-04
## [1137,] 0.259696720 0.4403553087 2.488965e-01
## [1138,] 0.397531973 0.3493462791 1.023338e-01
## [1139,] 0.424154946 0.3063341278 7.374710e-02
## [1140,] 0.275519452 0.4362391326 2.302373e-01
## [1141,] 0.426168977 0.1482326877 1.718640e-02
## [1142,] 0.204487093 0.0179374643 5.244873e-04
## [1143,] 0.377630828 0.0906313987 7.250512e-03
## [1144,] 0.444093854 0.2114732637 3.356718e-02
## [1145,] 0.243697761 0.4430868383 2.685375e-01
## [1146,] 0.438655970 0.1794501695 2.447048e-02
## [1147,] 0.386693968 0.3625255950 1.132892e-01
## [1148,] 0.433331375 0.1637029640 2.061445e-02
## [1149,] 0.169380014 0.0116813803 2.685375e-04
## [1150,] 0.362525595 0.3866939680 1.374912e-01
## [1151,] 0.243697761 0.4430868383 2.685375e-01
## [1152,] 0.090631399 0.0030210466 3.356718e-05
## [1153,] 0.444358195 0.2275981001 3.885821e-02
## [1154,] 0.406028666 0.1184250277 1.151354e-02
## [1155,] 0.236850055 0.0253767916 9.063140e-04
## [1156,] 0.321175019 0.4163379880 1.798991e-01
## [1157,] 0.433331375 0.1637029640 2.061445e-02
## [1158,] 0.236850055 0.0253767916 9.063140e-04
## [1159,] 0.259696720 0.4403553087 2.488965e-01
## [1160,] 0.430813836 0.2910904300 6.556091e-02
## [1161,] 0.417093250 0.1331148669 1.416116e-02
## [1162,] 0.443086838 0.2436977611 4.467792e-02
## [1163,] 0.444358195 0.2275981001 3.885821e-02
## [1164,] 0.433331375 0.1637029640 2.061445e-02
## [1165,] 0.433331375 0.1637029640 2.061445e-02
## [1166,] 0.259696720 0.4403553087 2.488965e-01
## [1167,] 0.386693968 0.3625255950 1.132892e-01
## [1168,] 0.440355309 0.2596967205 5.105149e-02
## [1169,] 0.227598100 0.4443581954 2.891855e-01
## [1170,] 0.291090430 0.4308138364 2.125348e-01
## [1171,] 0.306334128 0.4241549461 1.957638e-01
## [1172,] 0.426168977 0.1482326877 1.718640e-02
## [1173,] 0.430813836 0.2910904300 6.556091e-02
## [1174,] 0.430813836 0.2910904300 6.556091e-02
## [1175,] 0.179450170 0.4386559699 3.574234e-01
## [1176,] 0.416337988 0.3211750193 8.258786e-02
## [1177,] 0.443086838 0.2436977611 4.467792e-02
## [1178,] 0.417093250 0.1331148669 1.416116e-02
## [1179,] 0.416337988 0.3211750193 8.258786e-02
## [1180,] 0.131453291 0.0066840657 1.132892e-04
## [1181,] 0.306334128 0.4241549461 1.957638e-01
## [1182,] 0.430813836 0.2910904300 6.556091e-02
## [1183,] 0.306334128 0.4241549461 1.957638e-01
## [1184,] 0.433331375 0.1637029640 2.061445e-02
## [1185,] 0.430813836 0.2910904300 6.556091e-02
## [1186,] 0.133114867 0.4170932496 4.356307e-01
## [1187,] 0.236850055 0.0253767916 9.063140e-04
## [1188,] 0.416337988 0.3211750193 8.258786e-02
## [1189,] 0.438655970 0.1794501695 2.447048e-02
## [1190,] 0.416337988 0.3211750193 8.258786e-02
## [1191,] 0.417093250 0.1331148669 1.416116e-02
## [1192,] 0.442218287 0.1953987782 2.877966e-02
## [1193,] 0.204487093 0.0179374643 5.244873e-04
## [1194,] 0.195398778 0.4422182874 3.336033e-01
## [1195,] 0.397531973 0.3493462791 1.023338e-01
## [1196,] 0.360146521 0.0776786613 5.584740e-03
## [1197,] 0.442218287 0.1953987782 2.877966e-02
## [1198,] 0.259696720 0.4403553087 2.488965e-01
## [1199,] 0.444358195 0.2275981001 3.885821e-02
## [1200,] 0.227598100 0.4443581954 2.891855e-01
## [1201,] 0.392899701 0.1042386963 9.218388e-03
## [1202,] 0.293645732 0.0435030714 2.148300e-03
## [1203,] 0.349346279 0.3975319727 1.507880e-01
## [1204,] 0.362525595 0.3866939680 1.374912e-01
## [1205,] 0.406028666 0.1184250277 1.151354e-02
## [1206,] 0.211473264 0.4440938538 3.108657e-01
## [1207,] 0.440355309 0.2596967205 5.105149e-02
## [1208,] 0.406028666 0.1184250277 1.151354e-02
## [1209,] 0.293645732 0.0435030714 2.148300e-03
## [1210,] 0.440355309 0.2596967205 5.105149e-02
## [1211,] 0.362525595 0.3866939680 1.374912e-01
## [1212,] 0.430813836 0.2910904300 6.556091e-02
## [1213,] 0.046838810 0.0007678494 4.195898e-06
## [1214,] 0.436239133 0.2755194522 5.800410e-02
## [1215,] 0.321175019 0.4163379880 1.798991e-01
## [1216,] 0.169380014 0.0116813803 2.685375e-04
## [1217,] 0.375000000 0.3750000000 1.250000e-01
## [1218,] 0.417093250 0.1331148669 1.416116e-02
## [1219,] 0.392899701 0.1042386963 9.218388e-03
## [1220,] 0.430813836 0.2910904300 6.556091e-02
## [1221,] 0.259696720 0.4403553087 2.488965e-01
## [1222,] 0.386693968 0.3625255950 1.132892e-01
## [1223,] 0.243697761 0.4430868383 2.685375e-01
## [1224,] 0.362525595 0.3866939680 1.374912e-01
## [1225,] 0.335537578 0.4074384881 1.649156e-01
## [1226,] 0.386693968 0.3625255950 1.132892e-01
## [1227,] 0.321175019 0.4163379880 1.798991e-01
## [1228,] 0.430813836 0.2910904300 6.556091e-02
## [1229,] 0.266544426 0.0339238361 1.439193e-03
## [1230,] 0.433331375 0.1637029640 2.061445e-02
## [1231,] 0.438655970 0.1794501695 2.447048e-02
## [1232,] 0.430813836 0.2910904300 6.556091e-02
## [1233,] 0.440355309 0.2596967205 5.105149e-02
## [1234,] 0.335537578 0.4074384881 1.649156e-01
## [1235,] 0.386693968 0.3625255950 1.132892e-01
## [1236,] 0.349346279 0.3975319727 1.507880e-01
## [1237,] 0.442218287 0.1953987782 2.877966e-02
## [1238,] 0.386693968 0.3625255950 1.132892e-01
## [1239,] 0.436239133 0.2755194522 5.800410e-02
## [1240,] 0.430813836 0.2910904300 6.556091e-02
## [1241,] 0.444093854 0.2114732637 3.356718e-02
## [1242,] 0.204487093 0.0179374643 5.244873e-04
## [1243,] 0.306334128 0.4241549461 1.957638e-01
## [1244,] 0.118425028 0.4060286664 4.640328e-01
## [1245,] 0.397531973 0.3493462791 1.023338e-01
## [1246,] 0.433331375 0.1637029640 2.061445e-02
## [1247,] 0.433331375 0.1637029640 2.061445e-02
## [1248,] 0.443086838 0.2436977611 4.467792e-02
## [1249,] 0.440355309 0.2596967205 5.105149e-02
## [1250,] 0.443086838 0.2436977611 4.467792e-02
## [1251,] 0.362525595 0.3866939680 1.374912e-01
## [1252,] 0.433331375 0.1637029640 2.061445e-02
## [1253,] 0.430813836 0.2910904300 6.556091e-02
## [1254,] 0.293645732 0.0435030714 2.148300e-03
## [1255,] 0.195398778 0.4422182874 3.336033e-01
## [1256,] 0.362525595 0.3866939680 1.374912e-01
## [1257,] 0.169380014 0.0116813803 2.685375e-04
## [1258,] 0.179450170 0.4386559699 3.574234e-01
## [1259,] 0.291090430 0.4308138364 2.125348e-01
## [1260,] 0.360146521 0.0776786613 5.584740e-03
## [1261,] 0.444358195 0.2275981001 3.885821e-02
## [1262,] 0.054038972 0.3182294988 6.246727e-01
## [1263,] 0.169380014 0.0116813803 2.685375e-04
## [1264,] 0.386693968 0.3625255950 1.132892e-01
## [1265,] 0.433331375 0.1637029640 2.061445e-02
## [1266,] 0.407438488 0.3355375785 9.210835e-02
## [1267,] 0.291090430 0.4308138364 2.125348e-01
## [1268,] 0.438655970 0.1794501695 2.447048e-02
## [1269,] 0.259696720 0.4403553087 2.488965e-01
## [1270,] 0.211473264 0.4440938538 3.108657e-01
## [1271,] 0.440355309 0.2596967205 5.105149e-02
## [1272,] 0.275519452 0.4362391326 2.302373e-01
## [1273,] 0.406028666 0.1184250277 1.151354e-02
## [1274,] 0.438655970 0.1794501695 2.447048e-02
## [1275,] 0.340371253 0.0654560102 4.195898e-03
## [1276,] 0.211473264 0.4440938538 3.108657e-01
## [1277,] 0.440355309 0.2596967205 5.105149e-02
## [1278,] 0.291090430 0.4308138364 2.125348e-01
## [1279,] 0.407438488 0.3355375785 9.210835e-02
## [1280,] 0.179450170 0.4386559699 3.574234e-01
## [1281,] 0.424154946 0.3063341278 7.374710e-02
## [1282,] 0.438655970 0.1794501695 2.447048e-02
## [1283,] 0.440355309 0.2596967205 5.105149e-02
## [1284,] 0.169380014 0.0116813803 2.685375e-04
## [1285,] 0.349346279 0.3975319727 1.507880e-01
## [1286,] 0.259696720 0.4403553087 2.488965e-01
## [1287,] 0.291090430 0.4308138364 2.125348e-01
## [1288,] 0.438655970 0.1794501695 2.447048e-02
## [1289,] 0.406028666 0.1184250277 1.151354e-02
## [1290,] 0.438655970 0.1794501695 2.447048e-02
## [1291,] 0.340371253 0.0654560102 4.195898e-03
## [1292,] 0.444358195 0.2275981001 3.885821e-02
## [1293,] 0.436239133 0.2755194522 5.800410e-02
## [1294,] 0.291090430 0.4308138364 2.125348e-01
## [1295,] 0.444358195 0.2275981001 3.885821e-02
## [1296,] 0.436239133 0.2755194522 5.800410e-02
## [1297,] 0.417093250 0.1331148669 1.416116e-02
## [1298,] 0.204487093 0.0179374643 5.244873e-04
## [1299,] 0.259696720 0.4403553087 2.488965e-01
## [1300,] 0.318229499 0.0540389715 3.058810e-03
## [1301,] 0.266544426 0.0339238361 1.439193e-03
## [1302,] 0.318229499 0.0540389715 3.058810e-03
## [1303,] 0.417093250 0.1331148669 1.416116e-02
## [1304,] 0.169380014 0.0116813803 2.685375e-04
## [1305,] 0.397531973 0.3493462791 1.023338e-01
## [1306,] 0.397531973 0.3493462791 1.023338e-01
## [1307,] 0.392899701 0.1042386963 9.218388e-03
## [1308,] 0.407438488 0.3355375785 9.210835e-02
## [1309,] 0.397531973 0.3493462791 1.023338e-01
## [1310,] 0.443086838 0.2436977611 4.467792e-02
## [1311,] 0.349346279 0.3975319727 1.507880e-01
## [1312,] 0.392899701 0.1042386963 9.218388e-03
## [1313,] 0.243697761 0.4430868383 2.685375e-01
## [1314,] 0.386693968 0.3625255950 1.132892e-01
## [1315,] 0.306334128 0.4241549461 1.957638e-01
## [1316,] 0.275519452 0.4362391326 2.302373e-01
## [1317,] 0.195398778 0.4422182874 3.336033e-01
## [1318,] 0.406028666 0.1184250277 1.151354e-02
## [1319,] 0.211473264 0.4440938538 3.108657e-01
## [1320,] 0.436239133 0.2755194522 5.800410e-02
## [1321,] 0.321175019 0.4163379880 1.798991e-01
## [1322,] 0.406028666 0.1184250277 1.151354e-02
## [1323,] 0.362525595 0.3866939680 1.374912e-01
## [1324,] 0.443086838 0.2436977611 4.467792e-02
## [1325,] 0.436239133 0.2755194522 5.800410e-02
## [1326,] 0.433331375 0.1637029640 2.061445e-02
## [1327,] 0.417093250 0.1331148669 1.416116e-02
## [1328,] 0.417093250 0.1331148669 1.416116e-02
## [1329,] 0.444093854 0.2114732637 3.356718e-02
## [1330,] 0.436239133 0.2755194522 5.800410e-02
## [1331,] 0.243697761 0.4430868383 2.685375e-01
## [1332,] 0.416337988 0.3211750193 8.258786e-02
## [1333,] 0.377630828 0.0906313987 7.250512e-03
## [1334,] 0.426168977 0.1482326877 1.718640e-02
## [1335,] 0.430813836 0.2910904300 6.556091e-02
## [1336,] 0.424154946 0.3063341278 7.374710e-02
## [1337,] 0.340371253 0.0654560102 4.195898e-03
## [1338,] 0.407438488 0.3355375785 9.210835e-02
## [1339,] 0.438655970 0.1794501695 2.447048e-02
## [1340,] 0.442218287 0.1953987782 2.877966e-02
## [1341,] 0.397531973 0.3493462791 1.023338e-01
## [1342,] 0.444093854 0.2114732637 3.356718e-02
## [1343,] 0.440355309 0.2596967205 5.105149e-02
## [1344,] 0.179450170 0.4386559699 3.574234e-01
## [1345,] 0.443086838 0.2436977611 4.467792e-02
## [1346,] 0.424154946 0.3063341278 7.374710e-02
## [1347,] 0.275519452 0.4362391326 2.302373e-01
## [1348,] 0.349346279 0.3975319727 1.507880e-01
## [1349,] 0.335537578 0.4074384881 1.649156e-01
## [1350,] 0.318229499 0.0540389715 3.058810e-03
## [1351,] 0.335537578 0.4074384881 1.649156e-01
## [1352,] 0.349346279 0.3975319727 1.507880e-01
## [1353,] 0.340371253 0.0654560102 4.195898e-03
## [1354,] 0.375000000 0.3750000000 1.250000e-01
## [1355,] 0.195398778 0.4422182874 3.336033e-01
## [1356,] 0.204487093 0.0179374643 5.244873e-04
## [1357,] 0.321175019 0.4163379880 1.798991e-01
## [1358,] 0.291090430 0.4308138364 2.125348e-01
## [1359,] 0.386693968 0.3625255950 1.132892e-01
## [1360,] 0.362525595 0.3866939680 1.374912e-01
## [1361,] 0.392899701 0.1042386963 9.218388e-03
## [1362,] 0.321175019 0.4163379880 1.798991e-01
## [1363,] 0.430813836 0.2910904300 6.556091e-02
## [1364,] 0.090631399 0.0030210466 3.356718e-05
## [1365,] 0.407438488 0.3355375785 9.210835e-02
## [1366,] 0.275519452 0.4362391326 2.302373e-01
## [1367,] 0.424154946 0.3063341278 7.374710e-02
## [1368,] 0.204487093 0.0179374643 5.244873e-04
## [1369,] 0.436239133 0.2755194522 5.800410e-02
## [1370,] 0.406028666 0.1184250277 1.151354e-02
## [1371,] 0.430813836 0.2910904300 6.556091e-02
## [1372,] 0.259696720 0.4403553087 2.488965e-01
## [1373,] 0.104238696 0.3928997013 4.936432e-01
## [1374,] 0.375000000 0.3750000000 1.250000e-01
## [1375,] 0.360146521 0.0776786613 5.584740e-03
## [1376,] 0.433331375 0.1637029640 2.061445e-02
## [1377,] 0.444358195 0.2275981001 3.885821e-02
## [1378,] 0.417093250 0.1331148669 1.416116e-02
## [1379,] 0.321175019 0.4163379880 1.798991e-01
## [1380,] 0.430813836 0.2910904300 6.556091e-02
## [1381,] 0.438655970 0.1794501695 2.447048e-02
## [1382,] 0.444093854 0.2114732637 3.356718e-02
## [1383,] 0.243697761 0.4430868383 2.685375e-01
## [1384,] 0.416337988 0.3211750193 8.258786e-02
## [1385,] 0.426168977 0.1482326877 1.718640e-02
## [1386,] 0.377630828 0.0906313987 7.250512e-03
## [1387,] 0.131453291 0.0066840657 1.132892e-04
## [1388,] 0.236850055 0.0253767916 9.063140e-04
## [1389,] 0.386693968 0.3625255950 1.132892e-01
## [1390,] 0.392899701 0.1042386963 9.218388e-03
## [1391,] 0.424154946 0.3063341278 7.374710e-02
## [1392,] 0.377630828 0.0906313987 7.250512e-03
## [1393,] 0.406028666 0.1184250277 1.151354e-02
## [1394,] 0.444358195 0.2275981001 3.885821e-02
## [1395,] 0.436239133 0.2755194522 5.800410e-02
## [1396,] 0.236850055 0.0253767916 9.063140e-04
## [1397,] 0.424154946 0.3063341278 7.374710e-02
## [1398,] 0.377630828 0.0906313987 7.250512e-03
## [1399,] 0.243697761 0.4430868383 2.685375e-01
## [1400,] 0.275519452 0.4362391326 2.302373e-01
## [1401,] 0.340371253 0.0654560102 4.195898e-03
## [1402,] 0.169380014 0.0116813803 2.685375e-04
## [1403,] 0.442218287 0.1953987782 2.877966e-02
## [1404,] 0.000000000 0.0000000000 0.000000e+00
## [1405,] 0.430813836 0.2910904300 6.556091e-02
## [1406,] 0.438655970 0.1794501695 2.447048e-02
## [1407,] 0.397531973 0.3493462791 1.023338e-01
## [1408,] 0.335537578 0.4074384881 1.649156e-01
## [1409,] 0.426168977 0.1482326877 1.718640e-02
## [1410,] 0.179450170 0.4386559699 3.574234e-01
## [1411,] 0.386693968 0.3625255950 1.132892e-01
## [1412,] 0.433331375 0.1637029640 2.061445e-02
## [1413,] 0.436239133 0.2755194522 5.800410e-02
## [1414,] 0.426168977 0.1482326877 1.718640e-02
## [1415,] 0.362525595 0.3866939680 1.374912e-01
## [1416,] 0.362525595 0.3866939680 1.374912e-01
## [1417,] 0.275519452 0.4362391326 2.302373e-01
## [1418,] 0.362525595 0.3866939680 1.374912e-01
## [1419,] 0.424154946 0.3063341278 7.374710e-02
## [1420,] 0.377630828 0.0906313987 7.250512e-03
## [1421,] 0.426168977 0.1482326877 1.718640e-02
## [1422,] 0.362525595 0.3866939680 1.374912e-01
## [1423,] 0.349346279 0.3975319727 1.507880e-01
## [1424,] 0.443086838 0.2436977611 4.467792e-02
## [1425,] 0.426168977 0.1482326877 1.718640e-02
## [1426,] 0.438655970 0.1794501695 2.447048e-02
## [1427,] 0.424154946 0.3063341278 7.374710e-02
## [1428,] 0.438655970 0.1794501695 2.447048e-02
## [1429,] 0.179450170 0.4386559699 3.574234e-01
## [1430,] 0.417093250 0.1331148669 1.416116e-02
## [1431,] 0.424154946 0.3063341278 7.374710e-02
## [1432,] 0.000000000 0.0000000000 1.000000e+00
## [1433,] 0.416337988 0.3211750193 8.258786e-02
## [1434,] 0.243697761 0.4430868383 2.685375e-01
## [1435,] 0.349346279 0.3975319727 1.507880e-01
## [1436,] 0.340371253 0.0654560102 4.195898e-03
## [1437,] 0.442218287 0.1953987782 2.877966e-02
## [1438,] 0.275519452 0.4362391326 2.302373e-01
## [1439,] 0.275519452 0.4362391326 2.302373e-01
## [1440,] 0.426168977 0.1482326877 1.718640e-02
## [1441,] 0.438655970 0.1794501695 2.447048e-02
## [1442,] 0.416337988 0.3211750193 8.258786e-02
## [1443,] 0.438655970 0.1794501695 2.447048e-02
## [1444,] 0.204487093 0.0179374643 5.244873e-04
## [1445,] 0.417093250 0.1331148669 1.416116e-02
## [1446,] 0.386693968 0.3625255950 1.132892e-01
## [1447,] 0.340371253 0.0654560102 4.195898e-03
## [1448,] 0.442218287 0.1953987782 2.877966e-02
## [1449,] 0.169380014 0.0116813803 2.685375e-04
## [1450,] 0.211473264 0.4440938538 3.108657e-01
## [1451,] 0.377630828 0.0906313987 7.250512e-03
## [1452,] 0.362525595 0.3866939680 1.374912e-01
## [1453,] 0.291090430 0.4308138364 2.125348e-01
## [1454,] 0.293645732 0.0435030714 2.148300e-03
## [1455,] 0.436239133 0.2755194522 5.800410e-02
## [1456,] 0.054038972 0.3182294988 6.246727e-01
## [1457,] 0.417093250 0.1331148669 1.416116e-02
## [1458,] 0.375000000 0.3750000000 1.250000e-01
## [1459,] 0.416337988 0.3211750193 8.258786e-02
## [1460,] 0.440355309 0.2596967205 5.105149e-02
## [1461,] 0.227598100 0.4443581954 2.891855e-01
## [1462,] 0.417093250 0.1331148669 1.416116e-02
## [1463,] 0.204487093 0.0179374643 5.244873e-04
## [1464,] 0.406028666 0.1184250277 1.151354e-02
## [1465,] 0.377630828 0.0906313987 7.250512e-03
## [1466,] 0.306334128 0.4241549461 1.957638e-01
## [1467,] 0.362525595 0.3866939680 1.374912e-01
## [1468,] 0.259696720 0.4403553087 2.488965e-01
## [1469,] 0.377630828 0.0906313987 7.250512e-03
## [1470,] 0.406028666 0.1184250277 1.151354e-02
## [1471,] 0.386693968 0.3625255950 1.132892e-01
## [1472,] 0.392899701 0.1042386963 9.218388e-03
## [1473,] 0.362525595 0.3866939680 1.374912e-01
## [1474,] 0.397531973 0.3493462791 1.023338e-01
## [1475,] 0.442218287 0.1953987782 2.877966e-02
## [1476,] 0.236850055 0.0253767916 9.063140e-04
## [1477,] 0.321175019 0.4163379880 1.798991e-01
## [1478,] 0.444358195 0.2275981001 3.885821e-02
## [1479,] 0.397531973 0.3493462791 1.023338e-01
## [1480,] 0.438655970 0.1794501695 2.447048e-02
## [1481,] 0.426168977 0.1482326877 1.718640e-02
## [1482,] 0.416337988 0.3211750193 8.258786e-02
## [1483,] 0.211473264 0.4440938538 3.108657e-01
## [1484,] 0.430813836 0.2910904300 6.556091e-02
## [1485,] 0.433331375 0.1637029640 2.061445e-02
## [1486,] 0.362525595 0.3866939680 1.374912e-01
## [1487,] 0.275519452 0.4362391326 2.302373e-01
## [1488,] 0.433331375 0.1637029640 2.061445e-02
## [1489,] 0.204487093 0.0179374643 5.244873e-04
## [1490,] 0.416337988 0.3211750193 8.258786e-02
## [1491,] 0.306334128 0.4241549461 1.957638e-01
## [1492,] 0.436239133 0.2755194522 5.800410e-02
## [1493,] 0.349346279 0.3975319727 1.507880e-01
## [1494,] 0.375000000 0.3750000000 1.250000e-01
## [1495,] 0.386693968 0.3625255950 1.132892e-01
## [1496,] 0.362525595 0.3866939680 1.374912e-01
## [1497,] 0.442218287 0.1953987782 2.877966e-02
## [1498,] 0.444093854 0.2114732637 3.356718e-02
## [1499,] 0.243697761 0.4430868383 2.685375e-01
## [1500,] 0.349346279 0.3975319727 1.507880e-01
## [1501,] 0.349346279 0.3975319727 1.507880e-01
## [1502,] 0.424154946 0.3063341278 7.374710e-02
## [1503,] 0.430813836 0.2910904300 6.556091e-02
## [1504,] 0.227598100 0.4443581954 2.891855e-01
## [1505,] 0.195398778 0.4422182874 3.336033e-01
## [1506,] 0.443086838 0.2436977611 4.467792e-02
## [1507,] 0.291090430 0.4308138364 2.125348e-01
## [1508,] 0.440355309 0.2596967205 5.105149e-02
## [1509,] 0.118425028 0.4060286664 4.640328e-01
## [1510,] 0.195398778 0.4422182874 3.336033e-01
## [1511,] 0.426168977 0.1482326877 1.718640e-02
## [1512,] 0.440355309 0.2596967205 5.105149e-02
## [1513,] 0.386693968 0.3625255950 1.132892e-01
## [1514,] 0.306334128 0.4241549461 1.957638e-01
## [1515,] 0.424154946 0.3063341278 7.374710e-02
## [1516,] 0.259696720 0.4403553087 2.488965e-01
## [1517,] 0.321175019 0.4163379880 1.798991e-01
## [1518,] 0.179450170 0.4386559699 3.574234e-01
## [1519,] 0.443086838 0.2436977611 4.467792e-02
## [1520,] 0.444358195 0.2275981001 3.885821e-02
## [1521,] 0.416337988 0.3211750193 8.258786e-02
## [1522,] 0.440355309 0.2596967205 5.105149e-02
## [1523,] 0.293645732 0.0435030714 2.148300e-03
## [1524,] 0.335537578 0.4074384881 1.649156e-01
## [1525,] 0.392899701 0.1042386963 9.218388e-03
## [1526,] 0.163702964 0.4333313752 3.823512e-01
## [1527,] 0.436239133 0.2755194522 5.800410e-02
## [1528,] 0.335537578 0.4074384881 1.649156e-01
## [1529,] 0.444093854 0.2114732637 3.356718e-02
## [1530,] 0.360146521 0.0776786613 5.584740e-03
## [1531,] 0.436239133 0.2755194522 5.800410e-02
## [1532,] 0.407438488 0.3355375785 9.210835e-02
## [1533,] 0.131453291 0.0066840657 1.132892e-04
## [1534,] 0.436239133 0.2755194522 5.800410e-02
## [1535,] 0.386693968 0.3625255950 1.132892e-01
## [1536,] 0.306334128 0.4241549461 1.957638e-01
## [1537,] 0.000000000 0.0000000000 1.000000e+00
## [1538,] 0.442218287 0.1953987782 2.877966e-02
## [1539,] 0.440355309 0.2596967205 5.105149e-02
## [1540,] 0.442218287 0.1953987782 2.877966e-02
## [1541,] 0.306334128 0.4241549461 1.957638e-01
## [1542,] 0.444358195 0.2275981001 3.885821e-02
## [1543,] 0.131453291 0.0066840657 1.132892e-04
## [1544,] 0.227598100 0.4443581954 2.891855e-01
## [1545,] 0.360146521 0.0776786613 5.584740e-03
## [1546,] 0.360146521 0.0776786613 5.584740e-03
## [1547,] 0.416337988 0.3211750193 8.258786e-02
## [1548,] 0.321175019 0.4163379880 1.798991e-01
## [1549,] 0.275519452 0.4362391326 2.302373e-01
## [1550,] 0.131453291 0.0066840657 1.132892e-04
## [1551,] 0.444358195 0.2275981001 3.885821e-02
## [1552,] 0.377630828 0.0906313987 7.250512e-03
## [1553,] 0.436239133 0.2755194522 5.800410e-02
## [1554,] 0.443086838 0.2436977611 4.467792e-02
## [1555,] 0.397531973 0.3493462791 1.023338e-01
## [1556,] 0.430813836 0.2910904300 6.556091e-02
## [1557,] 0.436239133 0.2755194522 5.800410e-02
## [1558,] 0.444358195 0.2275981001 3.885821e-02
## [1559,] 0.362525595 0.3866939680 1.374912e-01
## [1560,] 0.211473264 0.4440938538 3.108657e-01
## [1561,] 0.259696720 0.4403553087 2.488965e-01
## [1562,] 0.444093854 0.2114732637 3.356718e-02
## [1563,] 0.375000000 0.3750000000 1.250000e-01
## [1564,] 0.349346279 0.3975319727 1.507880e-01
## [1565,] 0.417093250 0.1331148669 1.416116e-02
## [1566,] 0.227598100 0.4443581954 2.891855e-01
## [1567,] 0.440355309 0.2596967205 5.105149e-02
## [1568,] 0.417093250 0.1331148669 1.416116e-02
## [1569,] 0.340371253 0.0654560102 4.195898e-03
## [1570,] 0.375000000 0.3750000000 1.250000e-01
## [1571,] 0.293645732 0.0435030714 2.148300e-03
## [1572,] 0.169380014 0.0116813803 2.685375e-04
## [1573,] 0.397531973 0.3493462791 1.023338e-01
## [1574,] 0.227598100 0.4443581954 2.891855e-01
## [1575,] 0.416337988 0.3211750193 8.258786e-02
## [1576,] 0.444358195 0.2275981001 3.885821e-02
## [1577,] 0.438655970 0.1794501695 2.447048e-02
## [1578,] 0.195398778 0.4422182874 3.336033e-01
## [1579,] 0.426168977 0.1482326877 1.718640e-02
## [1580,] 0.335537578 0.4074384881 1.649156e-01
## [1581,] 0.417093250 0.1331148669 1.416116e-02
## [1582,] 0.438655970 0.1794501695 2.447048e-02
## [1583,] 0.444358195 0.2275981001 3.885821e-02
## [1584,] 0.227598100 0.4443581954 2.891855e-01
## [1585,] 0.443086838 0.2436977611 4.467792e-02
## [1586,] 0.375000000 0.3750000000 1.250000e-01
## [1587,] 0.444358195 0.2275981001 3.885821e-02
## [1588,] 0.443086838 0.2436977611 4.467792e-02
## [1589,] 0.204487093 0.0179374643 5.244873e-04
## [1590,] 0.046838810 0.0007678494 4.195898e-06
## [1591,] 0.397531973 0.3493462791 1.023338e-01
## [1592,] 0.430813836 0.2910904300 6.556091e-02
## [1593,] 0.443086838 0.2436977611 4.467792e-02
## [1594,] 0.444093854 0.2114732637 3.356718e-02
## [1595,] 0.163702964 0.4333313752 3.823512e-01
## [1596,] 0.416337988 0.3211750193 8.258786e-02
## [1597,] 0.442218287 0.1953987782 2.877966e-02
## [1598,] 0.440355309 0.2596967205 5.105149e-02
## [1599,] 0.416337988 0.3211750193 8.258786e-02
## [1600,] 0.169380014 0.0116813803 2.685375e-04
## [1601,] 0.243697761 0.4430868383 2.685375e-01
## [1602,] 0.424154946 0.3063341278 7.374710e-02
## [1603,] 0.443086838 0.2436977611 4.467792e-02
## [1604,] 0.417093250 0.1331148669 1.416116e-02
## [1605,] 0.433331375 0.1637029640 2.061445e-02
## [1606,] 0.163702964 0.4333313752 3.823512e-01
## [1607,] 0.440355309 0.2596967205 5.105149e-02
## [1608,] 0.416337988 0.3211750193 8.258786e-02
## [1609,] 0.433331375 0.1637029640 2.061445e-02
## [1610,] 0.335537578 0.4074384881 1.649156e-01
## [1611,] 0.397531973 0.3493462791 1.023338e-01
## [1612,] 0.443086838 0.2436977611 4.467792e-02
## [1613,] 0.386693968 0.3625255950 1.132892e-01
## [1614,] 0.360146521 0.0776786613 5.584740e-03
## [1615,] 0.375000000 0.3750000000 1.250000e-01
## [1616,] 0.406028666 0.1184250277 1.151354e-02
## [1617,] 0.440355309 0.2596967205 5.105149e-02
## [1618,] 0.243697761 0.4430868383 2.685375e-01
## [1619,] 0.440355309 0.2596967205 5.105149e-02
## [1620,] 0.426168977 0.1482326877 1.718640e-02
## [1621,] 0.430813836 0.2910904300 6.556091e-02
## [1622,] 0.407438488 0.3355375785 9.210835e-02
## [1623,] 0.433331375 0.1637029640 2.061445e-02
## [1624,] 0.436239133 0.2755194522 5.800410e-02
## [1625,] 0.397531973 0.3493462791 1.023338e-01
## [1626,] 0.416337988 0.3211750193 8.258786e-02
## [1627,] 0.426168977 0.1482326877 1.718640e-02
## [1628,] 0.259696720 0.4403553087 2.488965e-01
## [1629,] 0.349346279 0.3975319727 1.507880e-01
## [1630,] 0.318229499 0.0540389715 3.058810e-03
## [1631,] 0.426168977 0.1482326877 1.718640e-02
## [1632,] 0.386693968 0.3625255950 1.132892e-01
## [1633,] 0.204487093 0.0179374643 5.244873e-04
## [1634,] 0.440355309 0.2596967205 5.105149e-02
## [1635,] 0.375000000 0.3750000000 1.250000e-01
## [1636,] 0.397531973 0.3493462791 1.023338e-01
## [1637,] 0.362525595 0.3866939680 1.374912e-01
## [1638,] 0.291090430 0.4308138364 2.125348e-01
## [1639,] 0.416337988 0.3211750193 8.258786e-02
## [1640,] 0.169380014 0.0116813803 2.685375e-04
## [1641,] 0.436239133 0.2755194522 5.800410e-02
## [1642,] 0.397531973 0.3493462791 1.023338e-01
## [1643,] 0.386693968 0.3625255950 1.132892e-01
## [1644,] 0.349346279 0.3975319727 1.507880e-01
## [1645,] 0.243697761 0.4430868383 2.685375e-01
## [1646,] 0.406028666 0.1184250277 1.151354e-02
## [1647,] 0.375000000 0.3750000000 1.250000e-01
## [1648,] 0.033923836 0.2665444262 6.980925e-01
## [1649,] 0.000000000 0.0000000000 0.000000e+00
## [1650,] 0.340371253 0.0654560102 4.195898e-03
## [1651,] 0.349346279 0.3975319727 1.507880e-01
## [1652,] 0.424154946 0.3063341278 7.374710e-02
## [1653,] 0.424154946 0.3063341278 7.374710e-02
## [1654,] 0.386693968 0.3625255950 1.132892e-01
## [1655,] 0.179450170 0.4386559699 3.574234e-01
## [1656,] 0.306334128 0.4241549461 1.957638e-01
## [1657,] 0.386693968 0.3625255950 1.132892e-01
## [1658,] 0.033923836 0.2665444262 6.980925e-01
## [1659,] 0.377630828 0.0906313987 7.250512e-03
## [1660,] 0.440355309 0.2596967205 5.105149e-02
## [1661,] 0.443086838 0.2436977611 4.467792e-02
## [1662,] 0.306334128 0.4241549461 1.957638e-01
## [1663,] 0.417093250 0.1331148669 1.416116e-02
## [1664,] 0.392899701 0.1042386963 9.218388e-03
## [1665,] 0.416337988 0.3211750193 8.258786e-02
## [1666,] 0.443086838 0.2436977611 4.467792e-02
## [1667,] 0.392899701 0.1042386963 9.218388e-03
## [1668,] 0.046838810 0.0007678494 4.195898e-06
## [1669,] 0.430813836 0.2910904300 6.556091e-02
## [1670,] 0.275519452 0.4362391326 2.302373e-01
## [1671,] 0.375000000 0.3750000000 1.250000e-01
## [1672,] 0.436239133 0.2755194522 5.800410e-02
## [1673,] 0.318229499 0.0540389715 3.058810e-03
## [1674,] 0.426168977 0.1482326877 1.718640e-02
## [1675,] 0.397531973 0.3493462791 1.023338e-01
## [1676,] 0.433331375 0.1637029640 2.061445e-02
## [1677,] 0.417093250 0.1331148669 1.416116e-02
## [1678,] 0.433331375 0.1637029640 2.061445e-02
## [1679,] 0.443086838 0.2436977611 4.467792e-02
## [1680,] 0.321175019 0.4163379880 1.798991e-01
## [1681,] 0.426168977 0.1482326877 1.718640e-02
## [1682,] 0.407438488 0.3355375785 9.210835e-02
## [1683,] 0.424154946 0.3063341278 7.374710e-02
## [1684,] 0.444093854 0.2114732637 3.356718e-02
## [1685,] 0.438655970 0.1794501695 2.447048e-02
## [1686,] 0.318229499 0.0540389715 3.058810e-03
## [1687,] 0.417093250 0.1331148669 1.416116e-02
## [1688,] 0.275519452 0.4362391326 2.302373e-01
## [1689,] 0.417093250 0.1331148669 1.416116e-02
## [1690,] 0.406028666 0.1184250277 1.151354e-02
## [1691,] 0.444358195 0.2275981001 3.885821e-02
## [1692,] 0.321175019 0.4163379880 1.798991e-01
## [1693,] 0.438655970 0.1794501695 2.447048e-02
## [1694,] 0.443086838 0.2436977611 4.467792e-02
## [1695,] 0.349346279 0.3975319727 1.507880e-01
## [1696,] 0.443086838 0.2436977611 4.467792e-02
## [1697,] 0.275519452 0.4362391326 2.302373e-01
## [1698,] 0.362525595 0.3866939680 1.374912e-01
## [1699,] 0.375000000 0.3750000000 1.250000e-01
## [1700,] 0.406028666 0.1184250277 1.151354e-02
## [1701,] 0.386693968 0.3625255950 1.132892e-01
## [1702,] 0.406028666 0.1184250277 1.151354e-02
## [1703,] 0.377630828 0.0906313987 7.250512e-03
## [1704,] 0.377630828 0.0906313987 7.250512e-03
## [1705,] 0.417093250 0.1331148669 1.416116e-02
## [1706,] 0.275519452 0.4362391326 2.302373e-01
## [1707,] 0.407438488 0.3355375785 9.210835e-02
## [1708,] 0.375000000 0.3750000000 1.250000e-01
## [1709,] 0.236850055 0.0253767916 9.063140e-04
## [1710,] 0.386693968 0.3625255950 1.132892e-01
## [1711,] 0.321175019 0.4163379880 1.798991e-01
## [1712,] 0.426168977 0.1482326877 1.718640e-02
## [1713,] 0.275519452 0.4362391326 2.302373e-01
## [1714,] 0.443086838 0.2436977611 4.467792e-02
## [1715,] 0.266544426 0.0339238361 1.439193e-03
## [1716,] 0.433331375 0.1637029640 2.061445e-02
## [1717,] 0.443086838 0.2436977611 4.467792e-02
## [1718,] 0.362525595 0.3866939680 1.374912e-01
## [1719,] 0.386693968 0.3625255950 1.132892e-01
## [1720,] 0.443086838 0.2436977611 4.467792e-02
## [1721,] 0.416337988 0.3211750193 8.258786e-02
## [1722,] 0.377630828 0.0906313987 7.250512e-03
## [1723,] 0.426168977 0.1482326877 1.718640e-02
## [1724,] 0.406028666 0.1184250277 1.151354e-02
## [1725,] 0.321175019 0.4163379880 1.798991e-01
## [1726,] 0.406028666 0.1184250277 1.151354e-02
## [1727,] 0.444358195 0.2275981001 3.885821e-02
## [1728,] 0.349346279 0.3975319727 1.507880e-01
## [1729,] 0.118425028 0.4060286664 4.640328e-01
## [1730,] 0.438655970 0.1794501695 2.447048e-02
## [1731,] 0.416337988 0.3211750193 8.258786e-02
## [1732,] 0.442218287 0.1953987782 2.877966e-02
## [1733,] 0.375000000 0.3750000000 1.250000e-01
## [1734,] 0.321175019 0.4163379880 1.798991e-01
## [1735,] 0.118425028 0.4060286664 4.640328e-01
## [1736,] 0.243697761 0.4430868383 2.685375e-01
## [1737,] 0.306334128 0.4241549461 1.957638e-01
## [1738,] 0.236850055 0.0253767916 9.063140e-04
## [1739,] 0.179450170 0.4386559699 3.574234e-01
## [1740,] 0.163702964 0.4333313752 3.823512e-01
## [1741,] 0.416337988 0.3211750193 8.258786e-02
## [1742,] 0.204487093 0.0179374643 5.244873e-04
## [1743,] 0.392899701 0.1042386963 9.218388e-03
## [1744,] 0.424154946 0.3063341278 7.374710e-02
## [1745,] 0.430813836 0.2910904300 6.556091e-02
## [1746,] 0.386693968 0.3625255950 1.132892e-01
## [1747,] 0.291090430 0.4308138364 2.125348e-01
## [1748,] 0.416337988 0.3211750193 8.258786e-02
## [1749,] 0.386693968 0.3625255950 1.132892e-01
## [1750,] 0.163702964 0.4333313752 3.823512e-01
## [1751,] 0.259696720 0.4403553087 2.488965e-01
## [1752,] 0.077678661 0.3601465208 5.565901e-01
## [1753,] 0.392899701 0.1042386963 9.218388e-03
## [1754,] 0.430813836 0.2910904300 6.556091e-02
## [1755,] 0.046838810 0.0007678494 4.195898e-06
## [1756,] 0.424154946 0.3063341278 7.374710e-02
## [1757,] 0.360146521 0.0776786613 5.584740e-03
## [1758,] 0.293645732 0.0435030714 2.148300e-03
## [1759,] 0.442218287 0.1953987782 2.877966e-02
## [1760,] 0.377630828 0.0906313987 7.250512e-03
## [1761,] 0.424154946 0.3063341278 7.374710e-02
## [1762,] 0.386693968 0.3625255950 1.132892e-01
## [1763,] 0.442218287 0.1953987782 2.877966e-02
## [1764,] 0.377630828 0.0906313987 7.250512e-03
## [1765,] 0.407438488 0.3355375785 9.210835e-02
## [1766,] 0.442218287 0.1953987782 2.877966e-02
## [1767,] 0.243697761 0.4430868383 2.685375e-01
## [1768,] 0.335537578 0.4074384881 1.649156e-01
## [1769,] 0.436239133 0.2755194522 5.800410e-02
## [1770,] 0.407438488 0.3355375785 9.210835e-02
## [1771,] 0.430813836 0.2910904300 6.556091e-02
## [1772,] 0.438655970 0.1794501695 2.447048e-02
## [1773,] 0.443086838 0.2436977611 4.467792e-02
## [1774,] 0.090631399 0.0030210466 3.356718e-05
## [1775,] 0.406028666 0.1184250277 1.151354e-02
## [1776,] 0.392899701 0.1042386963 9.218388e-03
## [1777,] 0.340371253 0.0654560102 4.195898e-03
## [1778,] 0.440355309 0.2596967205 5.105149e-02
## [1779,] 0.436239133 0.2755194522 5.800410e-02
## [1780,] 0.046838810 0.0007678494 4.195898e-06
## [1781,] 0.148232688 0.4261689772 4.084119e-01
## [1782,] 0.442218287 0.1953987782 2.877966e-02
## [1783,] 0.236850055 0.0253767916 9.063140e-04
## [1784,] 0.293645732 0.0435030714 2.148300e-03
## [1785,] 0.424154946 0.3063341278 7.374710e-02
## [1786,] 0.444358195 0.2275981001 3.885821e-02
## [1787,] 0.321175019 0.4163379880 1.798991e-01
## [1788,] 0.436239133 0.2755194522 5.800410e-02
## [1789,] 0.424154946 0.3063341278 7.374710e-02
## [1790,] 0.266544426 0.0339238361 1.439193e-03
## [1791,] 0.407438488 0.3355375785 9.210835e-02
## [1792,] 0.377630828 0.0906313987 7.250512e-03
## [1793,] 0.444093854 0.2114732637 3.356718e-02
## [1794,] 0.362525595 0.3866939680 1.374912e-01
## [1795,] 0.204487093 0.0179374643 5.244873e-04
## [1796,] 0.407438488 0.3355375785 9.210835e-02
## [1797,] 0.195398778 0.4422182874 3.336033e-01
## [1798,] 0.227598100 0.4443581954 2.891855e-01
## [1799,] 0.259696720 0.4403553087 2.488965e-01
## [1800,] 0.266544426 0.0339238361 1.439193e-03
## [1801,] 0.386693968 0.3625255950 1.132892e-01
## [1802,] 0.335537578 0.4074384881 1.649156e-01
## [1803,] 0.424154946 0.3063341278 7.374710e-02
## [1804,] 0.443086838 0.2436977611 4.467792e-02
## [1805,] 0.430813836 0.2910904300 6.556091e-02
## [1806,] 0.430813836 0.2910904300 6.556091e-02
## [1807,] 0.436239133 0.2755194522 5.800410e-02
## [1808,] 0.438655970 0.1794501695 2.447048e-02
## [1809,] 0.438655970 0.1794501695 2.447048e-02
## [1810,] 0.054038972 0.3182294988 6.246727e-01
## [1811,] 0.090631399 0.0030210466 3.356718e-05
## [1812,] 0.204487093 0.0179374643 5.244873e-04
## [1813,] 0.436239133 0.2755194522 5.800410e-02
## [1814,] 0.440355309 0.2596967205 5.105149e-02
## [1815,] 0.318229499 0.0540389715 3.058810e-03
## [1816,] 0.360146521 0.0776786613 5.584740e-03
## [1817,] 0.169380014 0.0116813803 2.685375e-04
## [1818,] 0.444358195 0.2275981001 3.885821e-02
## [1819,] 0.362525595 0.3866939680 1.374912e-01
## [1820,] 0.436239133 0.2755194522 5.800410e-02
## [1821,] 0.444093854 0.2114732637 3.356718e-02
## [1822,] 0.291090430 0.4308138364 2.125348e-01
## [1823,] 0.397531973 0.3493462791 1.023338e-01
## [1824,] 0.335537578 0.4074384881 1.649156e-01
## [1825,] 0.275519452 0.4362391326 2.302373e-01
## [1826,] 0.377630828 0.0906313987 7.250512e-03
## [1827,] 0.407438488 0.3355375785 9.210835e-02
## [1828,] 0.430813836 0.2910904300 6.556091e-02
## [1829,] 0.077678661 0.3601465208 5.565901e-01
## [1830,] 0.090631399 0.3776308281 5.244873e-01
## [1831,] 0.444358195 0.2275981001 3.885821e-02
## [1832,] 0.118425028 0.4060286664 4.640328e-01
## [1833,] 0.377630828 0.0906313987 7.250512e-03
## [1834,] 0.375000000 0.3750000000 1.250000e-01
## [1835,] 0.306334128 0.4241549461 1.957638e-01
## [1836,] 0.386693968 0.3625255950 1.132892e-01
## [1837,] 0.442218287 0.1953987782 2.877966e-02
## [1838,] 0.407438488 0.3355375785 9.210835e-02
## [1839,] 0.321175019 0.4163379880 1.798991e-01
## [1840,] 0.000000000 0.0000000000 0.000000e+00
## [1841,] 0.375000000 0.3750000000 1.250000e-01
## [1842,] 0.444358195 0.2275981001 3.885821e-02
## [1843,] 0.443086838 0.2436977611 4.467792e-02
## [1844,] 0.442218287 0.1953987782 2.877966e-02
## [1845,] 0.236850055 0.0253767916 9.063140e-04
## [1846,] 0.433331375 0.1637029640 2.061445e-02
## [1847,] 0.424154946 0.3063341278 7.374710e-02
## [1848,] 0.443086838 0.2436977611 4.467792e-02
## [1849,] 0.444358195 0.2275981001 3.885821e-02
## [1850,] 0.436239133 0.2755194522 5.800410e-02
## [1851,] 0.442218287 0.1953987782 2.877966e-02
## [1852,] 0.243697761 0.4430868383 2.685375e-01
## [1853,] 0.443086838 0.2436977611 4.467792e-02
## [1854,] 0.318229499 0.0540389715 3.058810e-03
## [1855,] 0.392899701 0.1042386963 9.218388e-03
## [1856,] 0.424154946 0.3063341278 7.374710e-02
## [1857,] 0.444093854 0.2114732637 3.356718e-02
## [1858,] 0.440355309 0.2596967205 5.105149e-02
## [1859,] 0.291090430 0.4308138364 2.125348e-01
## [1860,] 0.444093854 0.2114732637 3.356718e-02
## [1861,] 0.417093250 0.1331148669 1.416116e-02
## [1862,] 0.430813836 0.2910904300 6.556091e-02
## [1863,] 0.266544426 0.0339238361 1.439193e-03
## [1864,] 0.443086838 0.2436977611 4.467792e-02
## [1865,] 0.430813836 0.2910904300 6.556091e-02
## [1866,] 0.436239133 0.2755194522 5.800410e-02
## [1867,] 0.444093854 0.2114732637 3.356718e-02
## [1868,] 0.424154946 0.3063341278 7.374710e-02
## [1869,] 0.046838810 0.0007678494 4.195898e-06
## [1870,] 0.424154946 0.3063341278 7.374710e-02
## [1871,] 0.406028666 0.1184250277 1.151354e-02
## [1872,] 0.433331375 0.1637029640 2.061445e-02
## [1873,] 0.426168977 0.1482326877 1.718640e-02
## [1874,] 0.211473264 0.4440938538 3.108657e-01
## [1875,] 0.306334128 0.4241549461 1.957638e-01
## [1876,] 0.392899701 0.1042386963 9.218388e-03
## [1877,] 0.397531973 0.3493462791 1.023338e-01
## [1878,] 0.433331375 0.1637029640 2.061445e-02
## [1879,] 0.433331375 0.1637029640 2.061445e-02
## [1880,] 0.442218287 0.1953987782 2.877966e-02
## [1881,] 0.318229499 0.0540389715 3.058810e-03
## [1882,] 0.148232688 0.4261689772 4.084119e-01
## [1883,] 0.335537578 0.4074384881 1.649156e-01
## [1884,] 0.293645732 0.0435030714 2.148300e-03
## [1885,] 0.440355309 0.2596967205 5.105149e-02
## [1886,] 0.169380014 0.0116813803 2.685375e-04
## [1887,] 0.407438488 0.3355375785 9.210835e-02
## [1888,] 0.444358195 0.2275981001 3.885821e-02
## [1889,] 0.204487093 0.0179374643 5.244873e-04
## [1890,] 0.375000000 0.3750000000 1.250000e-01
## [1891,] 0.424154946 0.3063341278 7.374710e-02
## [1892,] 0.090631399 0.0030210466 3.356718e-05
## [1893,] 0.430813836 0.2910904300 6.556091e-02
## [1894,] 0.436239133 0.2755194522 5.800410e-02
## [1895,] 0.417093250 0.1331148669 1.416116e-02
## [1896,] 0.179450170 0.4386559699 3.574234e-01
## [1897,] 0.430813836 0.2910904300 6.556091e-02
## [1898,] 0.407438488 0.3355375785 9.210835e-02
## [1899,] 0.000000000 0.0000000000 0.000000e+00
## [1900,] 0.430813836 0.2910904300 6.556091e-02
## [1901,] 0.424154946 0.3063341278 7.374710e-02
## [1902,] 0.204487093 0.0179374643 5.244873e-04
## [1903,] 0.438655970 0.1794501695 2.447048e-02
## [1904,] 0.443086838 0.2436977611 4.467792e-02
## [1905,] 0.293645732 0.0435030714 2.148300e-03
## [1906,] 0.293645732 0.0435030714 2.148300e-03
## [1907,] 0.397531973 0.3493462791 1.023338e-01
## [1908,] 0.243697761 0.4430868383 2.685375e-01
## [1909,] 0.259696720 0.4403553087 2.488965e-01
## [1910,] 0.377630828 0.0906313987 7.250512e-03
## [1911,] 0.424154946 0.3063341278 7.374710e-02
## [1912,] 0.360146521 0.0776786613 5.584740e-03
## [1913,] 0.442218287 0.1953987782 2.877966e-02
## [1914,] 0.426168977 0.1482326877 1.718640e-02
## [1915,] 0.362525595 0.3866939680 1.374912e-01
## [1916,] 0.444093854 0.2114732637 3.356718e-02
## [1917,] 0.291090430 0.4308138364 2.125348e-01
## [1918,] 0.444358195 0.2275981001 3.885821e-02
## [1919,] 0.291090430 0.4308138364 2.125348e-01
## [1920,] 0.436239133 0.2755194522 5.800410e-02
## [1921,] 0.444358195 0.2275981001 3.885821e-02
## [1922,] 0.397531973 0.3493462791 1.023338e-01
## [1923,] 0.443086838 0.2436977611 4.467792e-02
## [1924,] 0.349346279 0.3975319727 1.507880e-01
## [1925,] 0.340371253 0.0654560102 4.195898e-03
## [1926,] 0.321175019 0.4163379880 1.798991e-01
## [1927,] 0.306334128 0.4241549461 1.957638e-01
## [1928,] 0.349346279 0.3975319727 1.507880e-01
## [1929,] 0.417093250 0.1331148669 1.416116e-02
## [1930,] 0.291090430 0.4308138364 2.125348e-01
## [1931,] 0.424154946 0.3063341278 7.374710e-02
## [1932,] 0.443086838 0.2436977611 4.467792e-02
## [1933,] 0.293645732 0.0435030714 2.148300e-03
## [1934,] 0.430813836 0.2910904300 6.556091e-02
## [1935,] 0.430813836 0.2910904300 6.556091e-02
## [1936,] 0.424154946 0.3063341278 7.374710e-02
## [1937,] 0.426168977 0.1482326877 1.718640e-02
## [1938,] 0.349346279 0.3975319727 1.507880e-01
## [1939,] 0.436239133 0.2755194522 5.800410e-02
## [1940,] 0.211473264 0.4440938538 3.108657e-01
## [1941,] 0.438655970 0.1794501695 2.447048e-02
## [1942,] 0.211473264 0.4440938538 3.108657e-01
## [1943,] 0.169380014 0.0116813803 2.685375e-04
## [1944,] 0.440355309 0.2596967205 5.105149e-02
## [1945,] 0.275519452 0.4362391326 2.302373e-01
## [1946,] 0.375000000 0.3750000000 1.250000e-01
## [1947,] 0.416337988 0.3211750193 8.258786e-02
## [1948,] 0.335537578 0.4074384881 1.649156e-01
## [1949,] 0.377630828 0.0906313987 7.250512e-03
## [1950,] 0.360146521 0.0776786613 5.584740e-03
## [1951,] 0.204487093 0.0179374643 5.244873e-04
## [1952,] 0.386693968 0.3625255950 1.132892e-01
## [1953,] 0.424154946 0.3063341278 7.374710e-02
## [1954,] 0.179450170 0.4386559699 3.574234e-01
## [1955,] 0.417093250 0.1331148669 1.416116e-02
## [1956,] 0.349346279 0.3975319727 1.507880e-01
## [1957,] 0.204487093 0.0179374643 5.244873e-04
## [1958,] 0.397531973 0.3493462791 1.023338e-01
## [1959,] 0.426168977 0.1482326877 1.718640e-02
## [1960,] 0.426168977 0.1482326877 1.718640e-02
## [1961,] 0.430813836 0.2910904300 6.556091e-02
## [1962,] 0.443086838 0.2436977611 4.467792e-02
## [1963,] 0.321175019 0.4163379880 1.798991e-01
## [1964,] 0.406028666 0.1184250277 1.151354e-02
## [1965,] 0.386693968 0.3625255950 1.132892e-01
## [1966,] 0.443086838 0.2436977611 4.467792e-02
## [1967,] 0.430813836 0.2910904300 6.556091e-02
## [1968,] 0.275519452 0.4362391326 2.302373e-01
## [1969,] 0.291090430 0.4308138364 2.125348e-01
## [1970,] 0.444093854 0.2114732637 3.356718e-02
## [1971,] 0.443086838 0.2436977611 4.467792e-02
## [1972,] 0.444358195 0.2275981001 3.885821e-02
## [1973,] 0.362525595 0.3866939680 1.374912e-01
## [1974,] 0.377630828 0.0906313987 7.250512e-03
## [1975,] 0.275519452 0.4362391326 2.302373e-01
## [1976,] 0.430813836 0.2910904300 6.556091e-02
## [1977,] 0.430813836 0.2910904300 6.556091e-02
## [1978,] 0.104238696 0.3928997013 4.936432e-01
## [1979,] 0.362525595 0.3866939680 1.374912e-01
## [1980,] 0.227598100 0.4443581954 2.891855e-01
## [1981,] 0.349346279 0.3975319727 1.507880e-01
## [1982,] 0.306334128 0.4241549461 1.957638e-01
## [1983,] 0.025376792 0.2368500554 7.368668e-01
## [1984,] 0.335537578 0.4074384881 1.649156e-01
## [1985,] 0.442218287 0.1953987782 2.877966e-02
## [1986,] 0.266544426 0.0339238361 1.439193e-03
## [1987,] 0.118425028 0.4060286664 4.640328e-01
## [1988,] 0.397531973 0.3493462791 1.023338e-01
## [1989,] 0.424154946 0.3063341278 7.374710e-02
## [1990,] 0.442218287 0.1953987782 2.877966e-02
## [1991,] 0.406028666 0.1184250277 1.151354e-02
## [1992,] 0.430813836 0.2910904300 6.556091e-02
## [1993,] 0.293645732 0.0435030714 2.148300e-03
## [1994,] 0.444358195 0.2275981001 3.885821e-02
## [1995,] 0.416337988 0.3211750193 8.258786e-02
## [1996,] 0.443086838 0.2436977611 4.467792e-02
## [1997,] 0.349346279 0.3975319727 1.507880e-01
## [1998,] 0.335537578 0.4074384881 1.649156e-01
## [1999,] 0.430813836 0.2910904300 6.556091e-02
## [2000,] 0.340371253 0.0654560102 4.195898e-03
## [2001,] 0.293645732 0.0435030714 2.148300e-03
## [2002,] 0.416337988 0.3211750193 8.258786e-02
## [2003,] 0.426168977 0.1482326877 1.718640e-02
## [2004,] 0.033923836 0.2665444262 6.980925e-01
## [2005,] 0.392899701 0.1042386963 9.218388e-03
## [2006,] 0.360146521 0.0776786613 5.584740e-03
## [2007,] 0.443086838 0.2436977611 4.467792e-02
## [2008,] 0.436239133 0.2755194522 5.800410e-02
## [2009,] 0.362525595 0.3866939680 1.374912e-01
## [2010,] 0.349346279 0.3975319727 1.507880e-01
## [2011,] 0.266544426 0.0339238361 1.439193e-03
## [2012,] 0.321175019 0.4163379880 1.798991e-01
## [2013,] 0.443086838 0.2436977611 4.467792e-02
## [2014,] 0.424154946 0.3063341278 7.374710e-02
## [2015,] 0.417093250 0.1331148669 1.416116e-02
## [2016,] 0.360146521 0.0776786613 5.584740e-03
## [2017,] 0.318229499 0.0540389715 3.058810e-03
## [2018,] 0.443086838 0.2436977611 4.467792e-02
## [2019,] 0.438655970 0.1794501695 2.447048e-02
## [2020,] 0.275519452 0.4362391326 2.302373e-01
## [2021,] 0.426168977 0.1482326877 1.718640e-02
## [2022,] 0.195398778 0.4422182874 3.336033e-01
## [2023,] 0.444093854 0.2114732637 3.356718e-02
## [2024,] 0.291090430 0.4308138364 2.125348e-01
## [2025,] 0.236850055 0.0253767916 9.063140e-04
## [2026,] 0.169380014 0.0116813803 2.685375e-04
## [2027,] 0.444093854 0.2114732637 3.356718e-02
## [2028,] 0.360146521 0.0776786613 5.584740e-03
## [2029,] 0.377630828 0.0906313987 7.250512e-03
## [2030,] 0.444093854 0.2114732637 3.356718e-02
## [2031,] 0.375000000 0.3750000000 1.250000e-01
## [2032,] 0.054038972 0.3182294988 6.246727e-01
## [2033,] 0.406028666 0.1184250277 1.151354e-02
## [2034,] 0.406028666 0.1184250277 1.151354e-02
## [2035,] 0.443086838 0.2436977611 4.467792e-02
## [2036,] 0.266544426 0.0339238361 1.439193e-03
## [2037,] 0.438655970 0.1794501695 2.447048e-02
## [2038,] 0.227598100 0.4443581954 2.891855e-01
## [2039,] 0.375000000 0.3750000000 1.250000e-01
## [2040,] 0.436239133 0.2755194522 5.800410e-02
## [2041,] 0.227598100 0.4443581954 2.891855e-01
## [2042,] 0.318229499 0.0540389715 3.058810e-03
## [2043,] 0.377630828 0.0906313987 7.250512e-03
## [2044,] 0.306334128 0.4241549461 1.957638e-01
## [2045,] 0.426168977 0.1482326877 1.718640e-02
## [2046,] 0.397531973 0.3493462791 1.023338e-01
## [2047,] 0.360146521 0.0776786613 5.584740e-03
## [2048,] 0.440355309 0.2596967205 5.105149e-02
## [2049,] 0.377630828 0.0906313987 7.250512e-03
## [2050,] 0.433331375 0.1637029640 2.061445e-02
## [2051,] 0.169380014 0.0116813803 2.685375e-04
## [2052,] 0.442218287 0.1953987782 2.877966e-02
## [2053,] 0.179450170 0.4386559699 3.574234e-01
## [2054,] 0.397531973 0.3493462791 1.023338e-01
## [2055,] 0.349346279 0.3975319727 1.507880e-01
## [2056,] 0.397531973 0.3493462791 1.023338e-01
## [2057,] 0.340371253 0.0654560102 4.195898e-03
## [2058,] 0.436239133 0.2755194522 5.800410e-02
## [2059,] 0.406028666 0.1184250277 1.151354e-02
## [2060,] 0.426168977 0.1482326877 1.718640e-02
## [2061,] 0.444358195 0.2275981001 3.885821e-02
## [2062,] 0.424154946 0.3063341278 7.374710e-02
## [2063,] 0.444093854 0.2114732637 3.356718e-02
## [2064,] 0.386693968 0.3625255950 1.132892e-01
## [2065,] 0.443086838 0.2436977611 4.467792e-02
## [2066,] 0.318229499 0.0540389715 3.058810e-03
## [2067,] 0.436239133 0.2755194522 5.800410e-02
## [2068,] 0.377630828 0.0906313987 7.250512e-03
## [2069,] 0.360146521 0.0776786613 5.584740e-03
## [2070,] 0.386693968 0.3625255950 1.132892e-01
## [2071,] 0.275519452 0.4362391326 2.302373e-01
## [2072,] 0.424154946 0.3063341278 7.374710e-02
## [2073,] 0.266544426 0.0339238361 1.439193e-03
## [2074,] 0.349346279 0.3975319727 1.507880e-01
## [2075,] 0.362525595 0.3866939680 1.374912e-01
## [2076,] 0.426168977 0.1482326877 1.718640e-02
## [2077,] 0.377630828 0.0906313987 7.250512e-03
## [2078,] 0.426168977 0.1482326877 1.718640e-02
## [2079,] 0.436239133 0.2755194522 5.800410e-02
## [2080,] 0.362525595 0.3866939680 1.374912e-01
## [2081,] 0.360146521 0.0776786613 5.584740e-03
## [2082,] 0.169380014 0.0116813803 2.685375e-04
## [2083,] 0.306334128 0.4241549461 1.957638e-01
## [2084,] 0.407438488 0.3355375785 9.210835e-02
## [2085,] 0.433331375 0.1637029640 2.061445e-02
## [2086,] 0.321175019 0.4163379880 1.798991e-01
## [2087,] 0.195398778 0.4422182874 3.336033e-01
## [2088,] 0.443086838 0.2436977611 4.467792e-02
## [2089,] 0.335537578 0.4074384881 1.649156e-01
## [2090,] 0.443086838 0.2436977611 4.467792e-02
## [2091,] 0.275519452 0.4362391326 2.302373e-01
## [2092,] 0.444358195 0.2275981001 3.885821e-02
## [2093,] 0.243697761 0.4430868383 2.685375e-01
## [2094,] 0.349346279 0.3975319727 1.507880e-01
## [2095,] 0.406028666 0.1184250277 1.151354e-02
## [2096,] 0.362525595 0.3866939680 1.374912e-01
## [2097,] 0.293645732 0.0435030714 2.148300e-03
## [2098,] 0.433331375 0.1637029640 2.061445e-02
## [2099,] 0.392899701 0.1042386963 9.218388e-03
## [2100,] 0.318229499 0.0540389715 3.058810e-03
## [2101,] 0.318229499 0.0540389715 3.058810e-03
## [2102,] 0.291090430 0.4308138364 2.125348e-01
## attr(,"degree")
## [1] 3
## attr(,"knots")
## numeric(0)
## attr(,"Boundary.knots")
## [1] 18 80
## attr(,"intercept")
## [1] FALSE
## attr(,"class")
## [1] "bs"     "basis"  "matrix"

Preprocessing with Principal components Analysis (PCA)

library(caret); library(kernlab); data(spam)
inTrain <- createDataPartition(y=spam$type, p=0.75, list=F)
training <- spam[inTrain,]
testing <- spam[-inTrain,]

M <- abs(cor(training[,-58]))
diag(M) <-0
M

##                           make     address         all        num3d         our
## make              0.0000000000 0.010251209 0.061828339 0.0176950435 0.026331266
## address           0.0102512093 0.000000000 0.026773769 0.0068507758 0.016683052
## all               0.0618283393 0.026773769 0.000000000 0.0216824581 0.082098161
## num3d             0.0176950435 0.006850776 0.021682458 0.0000000000 0.004275045
## our               0.0263312660 0.016683052 0.082098161 0.0042750451 0.000000000
## over              0.0372724071 0.021004675 0.081774682 0.0101244830 0.047801736
## remove            0.0167515881 0.010897507 0.047687620 0.0224152935 0.143221602
## internet          0.0012151199 0.013973289 0.013450117 0.0103416281 0.034186181
## order             0.1134943267 0.001893951 0.090608549 0.0025842899 0.026563508
## mail              0.0345960678 0.040572652 0.019527914 0.0043898502 0.031458951
## receive           0.2086283343 0.003964620 0.048556647 0.0135189708 0.064343788
## will              0.1128220262 0.034898740 0.091902089 0.0186589766 0.073993294
## people            0.0682846394 0.013814191 0.035816398 0.0135387817 0.031968182
## report            0.0291515572 0.008384978 0.014349575 0.0148758373 0.020535265
## addresses         0.0244689899 0.005815296 0.130002639 0.0038876801 0.054531422
## free              0.0719434544 0.002773061 0.073851816 0.0013213185 0.078914775
## business          0.0926655219 0.012649729 0.039065009 0.0024621089 0.144718758
## email             0.0691401865 0.049155014 0.146911592 0.0229235213 0.056172228
## you               0.1155782605 0.052171562 0.126406713 0.0088493526 0.088369040
## credit            0.0333914604 0.014363981 0.053095905 0.0070320417 0.046283114
## your              0.1944882533 0.012591114 0.160496234 0.0113791925 0.139237460
## font              0.0250271596 0.007844967 0.037404564 0.0009053145 0.018877318
## num000            0.1477516176 0.022255004 0.131918124 0.0164370028 0.062257017
## money             0.1869624939 0.006545348 0.035877702 0.0360847491 0.002263030
## hp                0.0732837744 0.043205780 0.084047071 0.0155673639 0.070693056
## hpl               0.0657465404 0.038633414 0.058070039 0.0144755961 0.081387223
## george            0.0655791297 0.031841272 0.115118723 0.0111092111 0.090027679
## num650            0.0477349526 0.032807445 0.040002056 0.0110735373 0.064173502
## lab               0.0408811334 0.025851461 0.066682226 0.0081352263 0.039708810
## labs              0.0514955129 0.031657897 0.022922103 0.0107740192 0.050303828
## telnet            0.0418107334 0.025002650 0.028766814 0.0083742959 0.045041736
## num857            0.0333985953 0.012226956 0.061666464 0.0068682042 0.027812144
## data              0.0443333061 0.024976431 0.049210893 0.0089284257 0.045519318
## num415            0.0285884545 0.013442988 0.061875139 0.0069219127 0.027898639
## num85             0.0448420074 0.027043742 0.038328829 0.0058115439 0.049436261
## technology        0.0568828347 0.032238583 0.040633102 0.0067340265 0.059609413
## num1999           0.0527441834 0.028983211 0.067123679 0.0076574712 0.078170335
## parts             0.0066053559 0.008109559 0.004599206 0.0026619887 0.169924005
## pm                0.0040816927 0.021130918 0.019470565 0.0048502546 0.045788712
## direct            0.0339537101 0.018761386 0.051719521 0.0075776811 0.023081675
## cs                0.0192015997 0.014198192 0.033373935 0.0059309835 0.047818130
## meeting           0.0226410902 0.024563885 0.018844958 0.0084330703 0.108080213
## original          0.0212617938 0.012887794 0.046105743 0.0098702908 0.051327754
## project           0.0217837931 0.020186493 0.057490772 0.0063320855 0.013236186
## re                0.0322620540 0.012923461 0.049698541 0.0137213711 0.054742287
## edu               0.0465927300 0.021966367 0.057612428 0.0095447133 0.078028093
## table             0.0001682853 0.009709964 0.031790643 0.0035649647 0.028358916
## conference        0.0169282690 0.014601513 0.025684828 0.0010680297 0.028644973
## charSemicolon     0.0234496260 0.004667391 0.031405918 0.0033434846 0.032311366
## charRoundbracket  0.0270968221 0.044332185 0.021928697 0.0109288521 0.043127432
## charSquarebracket 0.0320951111 0.019144013 0.025380783 0.0069620421 0.025129534
## charExclamation   0.0537194124 0.010047941 0.097721623 0.0022715451 0.022652501
## charDollar        0.0904936815 0.004906670 0.083173895 0.0164271265 0.051387610
## charHash          0.0069572529 0.005652416 0.014205308 0.0024604911 0.008578909
## capitalAve        0.0435220815 0.003856182 0.087368825 0.0028276695 0.048970338
## capitalLong       0.0549154680 0.002322905 0.093170063 0.0165835615 0.043378064
## capitalTotal      0.0912654141 0.017607231 0.069090290 0.0184738663 0.001871741
##                          over      remove    internet       order         mail
## make              0.037272407 0.016751588 0.001215120 0.113494327 0.0345960678
## address           0.021004675 0.010897507 0.013973289 0.001893951 0.0405726524
## all               0.081774682 0.047687620 0.013450117 0.090608549 0.0195279137
## num3d             0.010124483 0.022415293 0.010341628 0.002584290 0.0043898502
## our               0.047801736 0.143221602 0.034186181 0.026563508 0.0314589507
## over              0.000000000 0.064394628 0.073772444 0.088073552 0.0096944487
## remove            0.064394628 0.000000000 0.044958066 0.060819064 0.0613709637
## internet          0.073772444 0.044958066 0.000000000 0.091520408 0.0819196124
## order             0.088073552 0.060819064 0.091520408 0.000000000 0.1167780269
## mail              0.009694449 0.061370964 0.081919612 0.116778027 0.0000000000
## receive           0.046773177 0.163354804 0.117996060 0.151434718 0.1187577175
## will              0.004722552 0.009819230 0.006489097 0.036763232 0.0660021364
## people            0.080358029 0.015441248 0.032167856 0.028852109 0.0317479284
## report            0.014199871 0.037980825 0.013882850 0.059089211 0.0112473007
## addresses         0.151944786 0.047293521 0.080947913 0.209954584 0.1181249133
## free              0.023026208 0.124402812 0.042530955 0.009363346 0.0227979372
## business          0.055256675 0.206929603 0.214506147 0.177347435 0.0891734071
## email             0.063459742 0.124857634 0.034767470 0.082268001 0.0287722530
## you               0.088101745 0.111935144 0.019079749 0.036852307 0.0844531544
## credit            0.073444945 0.064438080 0.139832829 0.163279777 0.0431160502
## your              0.105128000 0.136206660 0.158319171 0.152561170 0.0861879395
## font              0.001126507 0.001587305 0.015340427 0.016601930 0.0112261746
## num000            0.206701334 0.072286187 0.104220071 0.114860053 0.0686908583
## money             0.042958755 0.017758497 0.027994087 0.076478125 0.0469132857
## hp                0.082075416 0.089854049 0.052081649 0.065405857 0.0332712850
## hpl               0.087450205 0.081188429 0.044337430 0.047529626 0.0118708890
## george            0.067725585 0.067397200 0.058223680 0.062850198 0.0665629012
## num650            0.064875358 0.067513954 0.050349587 0.053818498 0.0199677906
## lab               0.048369147 0.049857592 0.037648173 0.044081310 0.0250833280
## labs              0.042535338 0.058755576 0.040434228 0.048623668 0.0173158453
## telnet            0.047563275 0.050564449 0.037973636 0.042184713 0.0226039245
## num857            0.035746110 0.040465509 0.034152681 0.031636782 0.0113226053
## data              0.036623164 0.042672854 0.040659495 0.019547455 0.0320050218
## num415            0.036216999 0.040860435 0.034713732 0.031328927 0.0103468095
## num85             0.051543217 0.052444862 0.033050993 0.040981497 0.0155220503
## technology        0.054679122 0.054688722 0.031817937 0.054886735 0.0201344669
## num1999           0.055360648 0.049418001 0.020826928 0.040251267 0.0042326049
## parts             0.015639505 0.014847481 0.011728024 0.006728179 0.0153984315
## pm                0.049406769 0.054360324 0.031304981 0.044614716 0.0153102187
## direct            0.028423658 0.030267384 0.003989796 0.004748995 0.0106407435
## cs                0.027263245 0.033662739 0.014061203 0.034877356 0.0295857132
## meeting           0.054348705 0.050856716 0.044766092 0.049348779 0.0540521268
## original          0.033481229 0.050071354 0.002455485 0.037385498 0.0237757219
## project           0.029571779 0.035609208 0.032214282 0.035538266 0.0288730877
## re                0.048493576 0.047735080 0.011810641 0.073419342 0.0244167127
## edu               0.029075222 0.057273985 0.042573518 0.056312806 0.0353694095
## table             0.014093876 0.018809532 0.011056631 0.009832825 0.0179683169
## conference        0.031098480 0.031688361 0.021651186 0.021941597 0.0125154224
## charSemicolon     0.024330392 0.034981046 0.029564174 0.016484387 0.0143464242
## charRoundbracket  0.002669307 0.046764497 0.028347606 0.031089928 0.0023222875
## charSquarebracket 0.025252787 0.026663804 0.017402882 0.005044004 0.0002322363
## charExclamation   0.050127304 0.052732146 0.032029857 0.036990272 0.0255748428
## charDollar        0.116330947 0.077013442 0.068971303 0.160183404 0.0642988962
## charHash          0.000734591 0.049583800 0.008571457 0.000100667 0.0470032475
## capitalAve        0.012650831 0.042162134 0.007765600 0.109668326 0.0614440165
## capitalLong       0.066904166 0.058170200 0.031876797 0.166952879 0.0825353125
## capitalTotal      0.071008242 0.003060082 0.045135091 0.263410332 0.0889325803
##                       receive        will      people       report    addresses
## make              0.208628334 0.112822026 0.068284639 0.0291515572 0.0244689899
## address           0.003964620 0.034898740 0.013814191 0.0083849777 0.0058152964
## all               0.048556647 0.091902089 0.035816398 0.0143495748 0.1300026393
## num3d             0.013518971 0.018658977 0.013538782 0.0148758373 0.0038876801
## our               0.064343788 0.073993294 0.031968182 0.0205352655 0.0545314220
## over              0.046773177 0.004722552 0.080358029 0.0141998706 0.1519447859
## remove            0.163354804 0.009819230 0.015441248 0.0379808249 0.0472935208
## internet          0.117996060 0.006489097 0.032167856 0.0138828504 0.0809479131
## order             0.151434718 0.036763232 0.028852109 0.0590892108 0.2099545845
## mail              0.118757717 0.066002136 0.031747928 0.0112473007 0.1181249133
## receive           0.000000000 0.129636358 0.053219651 0.0464950523 0.0531868897
## will              0.129636358 0.000000000 0.001420001 0.0025401745 0.0239228735
## people            0.053219651 0.001420001 0.000000000 0.0615657591 0.0817192610
## report            0.046495052 0.002540175 0.061565759 0.0000000000 0.0164038293
## addresses         0.053186890 0.023922874 0.081719261 0.0164038293 0.0000000000
## free              0.093636155 0.028007217 0.013514384 0.0010681457 0.0023805507
## business          0.191888288 0.055482171 0.056782182 0.0101168020 0.0302974900
## email             0.085967381 0.014085324 0.079987784 0.0362571322 0.2372871534
## you               0.141840248 0.092387108 0.118101556 0.0010949721 0.0505959402
## credit            0.180013164 0.020901042 0.014665439 0.0376544275 0.0212104542
## your              0.312171964 0.111752533 0.049889845 0.0240675883 0.0764059360
## font              0.009577142 0.046003846 0.030262341 0.0194650964 0.0002891061
## num000            0.088745311 0.020950843 0.129080292 0.0422022974 0.3182741315
## money             0.053061606 0.015093419 0.074035990 0.0244209007 0.0247752152
## hp                0.076139225 0.036101365 0.062056596 0.0319574904 0.0487448113
## hpl               0.074958460 0.011770562 0.073689583 0.0395249603 0.0287859302
## george            0.064939321 0.120844884 0.051724123 0.0284052318 0.0424128188
## num650            0.059452852 0.040544374 0.059673484 0.0171771205 0.0368262573
## lab               0.046759674 0.087845895 0.039226651 0.0078960121 0.0293510482
## labs              0.051554547 0.009330391 0.051358282 0.0251590749 0.0342526578
## telnet            0.040881908 0.028944345 0.040771148 0.0167855876 0.0283476607
## num857            0.037159896 0.051594095 0.031114073 0.0164443105 0.0224575272
## data              0.044537033 0.023426848 0.048699549 0.0191681429 0.0141591128
## num415            0.036648119 0.052430754 0.031062674 0.0166239733 0.0228858667
## num85             0.046182680 0.043401976 0.047721516 0.0220618948 0.0244580315
## technology        0.050903960 0.010979056 0.047398260 0.0010306766 0.0345278983
## num1999           0.036624325 0.045194093 0.035156028 0.0297705005 0.0420234736
## parts             0.008194087 0.022279363 0.012822224 0.0032763603 0.0116277689
## pm                0.050236472 0.018061298 0.022945338 0.0268364638 0.0127013497
## direct            0.022238307 0.035498256 0.009762093 0.0215613311 0.0533315436
## cs                0.034314353 0.035217500 0.017686443 0.0208261136 0.0118153462
## meeting           0.046075282 0.089723522 0.041943574 0.0024653224 0.0333174229
## original          0.037921655 0.029392153 0.008432761 0.0013915805 0.0379183342
## project           0.037104643 0.009005748 0.026224512 0.0120694916 0.0181473598
## re                0.060638900 0.077606950 0.048017732 0.0053992897 0.0364192112
## edu               0.051316908 0.070626129 0.020148695 0.0200793185 0.0254153346
## table             0.020094033 0.005269911 0.013259450 0.0517511215 0.0118961147
## conference        0.021181507 0.027479587 0.019572056 0.0150413172 0.0216183606
## charSemicolon     0.034470380 0.030414906 0.026641783 0.0194226684 0.0171486112
## charRoundbracket  0.057802577 0.034819391 0.044720646 0.0017080361 0.0062274193
## charSquarebracket 0.029728145 0.044557371 0.027338471 0.0119549956 0.0098634679
## charExclamation   0.024833733 0.007914177 0.043138964 0.0106750408 0.0097207012
## charDollar        0.074915892 0.019137779 0.188727334 0.0843707853 0.1206633337
## charHash          0.005154212 0.029376004 0.014696770 0.0056242600 0.0036064878
## capitalAve        0.027516687 0.013508605 0.013587433 0.0008744141 0.0095910319
## capitalLong       0.078404329 0.012819329 0.038957119 0.0453058252 0.1819834471
## capitalTotal      0.118877151 0.019688974 0.115553071 0.1702989353 0.1631348647
##                          free    business       email          you      credit
## make              0.071943454 0.092665522 0.069140187 0.1155782605 0.033391460
## address           0.002773061 0.012649729 0.049155014 0.0521715625 0.014363981
## all               0.073851816 0.039065009 0.146911592 0.1264067132 0.053095905
## num3d             0.001321319 0.002462109 0.022923521 0.0088493526 0.007032042
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## remove            0.124402812 0.206929603 0.124857634 0.1119351444 0.064438080
## internet          0.042530955 0.214506147 0.034767470 0.0190797492 0.139832829
## order             0.009363346 0.177347435 0.082268001 0.0368523070 0.163279777
## mail              0.022797937 0.089173407 0.028772253 0.0844531544 0.043116050
## receive           0.093636155 0.191888288 0.085967381 0.1418402484 0.180013164
## will              0.028007217 0.055482171 0.014085324 0.0923871079 0.020901042
## people            0.013514384 0.056782182 0.079987784 0.1181015556 0.014665439
## report            0.001068146 0.010116802 0.036257132 0.0010949721 0.037654428
## addresses         0.002380551 0.030297490 0.237287153 0.0505959402 0.021210454
## free              0.000000000 0.054539458 0.081208238 0.0812718813 0.032922983
## business          0.054539458 0.000000000 0.041601178 0.0886897639 0.227126479
## email             0.081208238 0.041601178 0.000000000 0.1009530904 0.016249200
## you               0.081271881 0.088689764 0.100953090 0.0000000000 0.054217806
## credit            0.032922983 0.227126479 0.016249200 0.0542178058 0.000000000
## your              0.096338953 0.217135107 0.134580032 0.3014571987 0.168526766
## font              0.008707616 0.019517714 0.025535193 0.0289412131 0.039684728
## num000            0.056532443 0.119800991 0.088915784 0.1146470747 0.056755794
## money             0.100173732 0.029886620 0.095020091 0.1908377416 0.063797918
## hp                0.088963160 0.052702509 0.044955435 0.1960142562 0.053481746
## hpl               0.078948716 0.078008151 0.027994126 0.1643506806 0.057435920
## george            0.017823007 0.068254782 0.070985272 0.1511038176 0.043723123
## num650            0.062258659 0.062085383 0.029506897 0.1150326541 0.043822641
## lab               0.046787628 0.046509080 0.052012392 0.0865283297 0.032832083
## labs              0.058403360 0.044590283 0.014515842 0.1137422902 0.042970658
## telnet            0.047379357 0.045331134 0.033811708 0.0967948604 0.033194231
## num857            0.039947928 0.041157248 0.041984220 0.0776295277 0.026848323
## data              0.043824348 0.039712487 0.048333428 0.1047163932 0.033176207
## num415            0.039770286 0.041218508 0.043301996 0.0777532347 0.027831235
## num85             0.053818954 0.052441298 0.008290727 0.0888403936 0.034976818
## technology        0.059722867 0.034530411 0.015384285 0.1322212462 0.043115904
## num1999           0.062992881 0.046301858 0.048193156 0.1246375605 0.046785730
## parts             0.014407937 0.014484541 0.012958314 0.0279322305 0.025677517
## pm                0.045511554 0.044722852 0.022694073 0.0394986529 0.036112861
## direct            0.032566834 0.003564518 0.005289105 0.0591020241 0.001162255
## cs                0.031790308 0.035391795 0.031391742 0.0600787151 0.023920476
## meeting           0.034294724 0.040000985 0.052125835 0.0895906246 0.033840677
## original          0.045552881 0.050457931 0.016862922 0.0491230666 0.033013341
## project           0.031455697 0.024360853 0.033732521 0.0647033282 0.014925420
## re                0.042217844 0.057029883 0.050587250 0.1342495085 0.050045384
## edu               0.048828920 0.056466401 0.039580156 0.0193717564 0.035650299
## table             0.018980459 0.007527992 0.026422653 0.0043056113 0.009270122
## conference        0.026127200 0.027774124 0.030395085 0.0570889525 0.021499438
## charSemicolon     0.028028954 0.036755121 0.040884295 0.0490592788 0.024959294
## charRoundbracket  0.041281177 0.030050331 0.035648846 0.1200763595 0.022689596
## charSquarebracket 0.028431189 0.033512035 0.022232301 0.0612986732 0.011685189
## charExclamation   0.101384013 0.069930532 0.042878940 0.1551444733 0.057577450
## charDollar        0.030032971 0.106528945 0.077914958 0.0935789113 0.053215397
## charHash          0.037138038 0.003104082 0.030605964 0.0034968813 0.012477741
## capitalAve        0.016932172 0.038999057 0.009477003 0.0319921946 0.075779888
## capitalLong       0.025267210 0.059610923 0.060054963 0.0007916675 0.112274228
## capitalTotal      0.001296509 0.075893961 0.043006876 0.0084561133 0.108440280
##                          your         font      num000        money
## make              0.194488253 2.502716e-02 0.147751618 0.1869624939
## address           0.012591114 7.844967e-03 0.022255004 0.0065453482
## all               0.160496234 3.740456e-02 0.131918124 0.0358777025
## num3d             0.011379193 9.053145e-04 0.016437003 0.0360847491
## our               0.139237460 1.887732e-02 0.062257017 0.0022630302
## over              0.105128000 1.126507e-03 0.206701334 0.0429587548
## remove            0.136206660 1.587305e-03 0.072286187 0.0177584967
## internet          0.158319171 1.534043e-02 0.104220071 0.0279940870
## order             0.152561170 1.660193e-02 0.114860053 0.0764781251
## mail              0.086187940 1.122617e-02 0.068690858 0.0469132857
## receive           0.312171964 9.577142e-03 0.088745311 0.0530616060
## will              0.111752533 4.600385e-02 0.020950843 0.0150934192
## people            0.049889845 3.026234e-02 0.129080292 0.0740359899
## report            0.024067588 1.946510e-02 0.042202297 0.0244209007
## addresses         0.076405936 2.891061e-04 0.318274131 0.0247752152
## free              0.096338953 8.707616e-03 0.056532443 0.1001737321
## business          0.217135107 1.951771e-02 0.119800991 0.0298866204
## email             0.134580032 2.553519e-02 0.088915784 0.0950200907
## you               0.301457199 2.894121e-02 0.114647075 0.1908377416
## credit            0.168526766 3.968473e-02 0.056755794 0.0637979178
## your              0.000000000 2.282683e-02 0.125467117 0.1550432120
## font              0.022826831 0.000000e+00 0.037658362 0.0102004261
## num000            0.125467117 3.765836e-02 0.000000000 0.0482613317
## money             0.155043212 1.020043e-02 0.048261332 0.0000000000
## hp                0.153217539 4.004337e-02 0.089148295 0.0642833175
## hpl               0.135575961 3.693815e-02 0.084385525 0.0603794824
## george            0.126719392 2.855565e-02 0.069458380 0.0461961429
## num650            0.096665789 2.866109e-02 0.069385904 0.0460912910
## lab               0.063871917 2.096628e-02 0.048893764 0.0347390773
## labs              0.089840313 2.795324e-02 0.064115382 0.0452744552
## telnet            0.072128125 2.151698e-02 0.051945166 0.0345520739
## num857            0.044352938 1.764722e-02 0.043037297 0.0284226853
## data              0.092220991 2.120913e-02 0.051936593 0.0359594025
## num415            0.045080348 1.789298e-02 0.043250174 0.0291410322
## num85             0.082170020 2.360646e-02 0.052658259 0.0364921342
## technology        0.107153430 2.819024e-02 0.065586677 0.0456273399
## num1999           0.115663508 3.494836e-02 0.071380314 0.0542458905
## parts             0.018352112 4.000192e-03 0.017330348 0.0055066200
## pm                0.070949591 2.337354e-02 0.039592380 0.0367560668
## direct            0.015045202 2.213905e-02 0.001973227 0.0251389647
## cs                0.060640198 1.523912e-02 0.036919559 0.0252129303
## meeting           0.089493901 2.166306e-02 0.052567099 0.0351486340
## original          0.048422841 2.240113e-02 0.046161090 0.0384593639
## project           0.060022849 1.249552e-02 0.036806994 0.0233003128
## re                0.038424376 3.333617e-02 0.056411042 0.0470765497
## edu               0.079663957 2.167025e-02 0.057198295 0.0303988081
## table             0.018138044 9.159848e-03 0.018611018 0.0114761353
## conference        0.048153207 1.394118e-02 0.030788001 0.0173104351
## charSemicolon     0.059984600 3.993788e-01 0.028201810 0.0173270199
## charRoundbracket  0.076237209 4.369711e-02 0.035515731 0.0290302370
## charSquarebracket 0.054176291 4.303239e-05 0.029123435 0.0210151706
## charExclamation   0.071457165 4.815566e-03 0.067371022 0.0462515983
## charDollar        0.158340476 7.545806e-03 0.330162221 0.0891438498
## charHash          0.004700013 1.998387e-01 0.013174929 0.0001303144
## capitalAve        0.032371759 2.054459e-02 0.006282975 0.0066877024
## capitalLong       0.064074564 3.016705e-02 0.114980943 0.0333474118
## capitalTotal      0.049735204 1.343887e-01 0.186256490 0.0738845041
##                             hp         hpl       george      num650         lab
## make              0.0732837744 0.065746540 0.0655791297 0.047734953 0.040881133
## address           0.0432057796 0.038633414 0.0318412715 0.032807445 0.025851461
## all               0.0840470709 0.058070039 0.1151187232 0.040002056 0.066682226
## num3d             0.0155673639 0.014475596 0.0111092111 0.011073537 0.008135226
## our               0.0706930565 0.081387223 0.0900276791 0.064173502 0.039708810
## over              0.0820754165 0.087450205 0.0677255850 0.064875358 0.048369147
## remove            0.0898540495 0.081188429 0.0673971998 0.067513954 0.049857592
## internet          0.0520816486 0.044337430 0.0582236797 0.050349587 0.037648173
## order             0.0654058571 0.047529626 0.0628501978 0.053818498 0.044081310
## mail              0.0332712850 0.011870889 0.0665629012 0.019967791 0.025083328
## receive           0.0761392255 0.074958460 0.0649393207 0.059452852 0.046759674
## will              0.0361013653 0.011770562 0.1208448844 0.040544374 0.087845895
## people            0.0620565959 0.073689583 0.0517241234 0.059673484 0.039226651
## report            0.0319574904 0.039524960 0.0284052318 0.017177121 0.007896012
## addresses         0.0487448113 0.028785930 0.0424128188 0.036826257 0.029351048
## free              0.0889631596 0.078948716 0.0178230068 0.062258659 0.046787628
## business          0.0527025089 0.078008151 0.0682547822 0.062085383 0.046509080
## email             0.0449554352 0.027994126 0.0709852718 0.029506897 0.052012392
## you               0.1960142562 0.164350681 0.1511038176 0.115032654 0.086528330
## credit            0.0534817463 0.057435920 0.0437231233 0.043822641 0.032832083
## your              0.1532175392 0.135575961 0.1267193924 0.096665789 0.063871917
## font              0.0400433670 0.036938154 0.0285556461 0.028661093 0.020966279
## num000            0.0891482946 0.084385525 0.0694583797 0.069385904 0.048893764
## money             0.0642833175 0.060379482 0.0461961429 0.046091291 0.034739077
## hp                0.0000000000 0.538998750 0.0077490625 0.332284739 0.191388498
## hpl               0.5389987501 0.000000000 0.0025146743 0.397323763 0.205866487
## george            0.0077490625 0.002514674 0.0000000000 0.037288018 0.029599567
## num650            0.3322847395 0.397323763 0.0372880182 0.000000000 0.351559246
## lab               0.1913884984 0.205866487 0.0295995670 0.351559246 0.000000000
## labs              0.4309240379 0.402719193 0.0481055122 0.612920904 0.380208098
## telnet            0.3741331777 0.388756795 0.0603270857 0.602261710 0.435124072
## num857            0.3582410628 0.374376711 0.0824218520 0.584175561 0.489207043
## data              0.0095937503 0.001841254 0.0229736101 0.020134009 0.001877568
## num415            0.3567309208 0.373270913 0.0816868077 0.582070224 0.487163907
## num85             0.2855628002 0.326746219 0.0331642279 0.568367428 0.305995466
## technology        0.3785356473 0.355187043 0.0391577118 0.572498951 0.391055830
## num1999           0.1239079707 0.179212795 0.0161213237 0.024354731 0.007269186
## parts             0.0201102621 0.046368807 0.0116820397 0.012254382 0.005330146
## pm                0.0687685115 0.078354862 0.0005318936 0.061761110 0.012195157
## direct            0.3224992138 0.335954047 0.0626456444 0.541601990 0.454287540
## cs                0.0055684926 0.020885795 0.0165949403 0.031910257 0.015851131
## meeting           0.0096678348 0.057950153 0.0009518897 0.006167762 0.424315315
## original          0.0952705312 0.124361546 0.0118348640 0.081544803 0.045520385
## project           0.0003021006 0.018155852 0.0136922371 0.004159053 0.002266160
## re                0.0578359069 0.003020758 0.0011082692 0.005835609 0.010421612
## edu               0.0452423719 0.037513177 0.0388828497 0.003024687 0.023140738
## table             0.0034161120 0.019412743 0.0096917006 0.007988997 0.001704075
## conference        0.0078789089 0.003015458 0.0113507246 0.010201337 0.001558340
## charSemicolon     0.0363940603 0.019216374 0.0256395518 0.023614441 0.019178061
## charRoundbracket  0.1365025373 0.150143639 0.0292647549 0.289765958 0.146921423
## charSquarebracket 0.0341615218 0.066973651 0.0164289374 0.035347544 0.002796885
## charExclamation   0.0857732454 0.081665090 0.0639839943 0.059859369 0.040759731
## charDollar        0.0903580199 0.087225900 0.0729119124 0.061774374 0.053702088
## charHash          0.0495873747 0.021915830 0.0216742580 0.011562897 0.004719951
## capitalAve        0.0175432622 0.023928300 0.0249796876 0.012626378 0.015173581
## capitalLong       0.0466030161 0.047583151 0.0505768235 0.034622372 0.032824071
## capitalTotal      0.0415675008 0.059879645 0.1033581926 0.070187447 0.061390160
##                           labs       telnet      num857         data
## make              0.0514955129 0.0418107334 0.033398595 0.0443333061
## address           0.0316578967 0.0250026497 0.012226956 0.0249764314
## all               0.0229221034 0.0287668137 0.061666464 0.0492108933
## num3d             0.0107740192 0.0083742959 0.006868204 0.0089284257
## our               0.0503038283 0.0450417364 0.027812144 0.0455193181
## over              0.0425353378 0.0475632746 0.035746110 0.0366231636
## remove            0.0587555764 0.0505644487 0.040465509 0.0426728542
## internet          0.0404342284 0.0379736363 0.034152681 0.0406594948
## order             0.0486236680 0.0421847135 0.031636782 0.0195474550
## mail              0.0173158453 0.0226039245 0.011322605 0.0320050218
## receive           0.0515545467 0.0408819075 0.037159896 0.0445370331
## will              0.0093303905 0.0289443449 0.051594095 0.0234268483
## people            0.0513582815 0.0407711483 0.031114073 0.0486995494
## report            0.0251590749 0.0167855876 0.016444310 0.0191681429
## addresses         0.0342526578 0.0283476607 0.022457527 0.0141591128
## free              0.0584033600 0.0473793568 0.039947928 0.0438243478
## business          0.0445902832 0.0453311337 0.041157248 0.0397124871
## email             0.0145158416 0.0338117081 0.041984220 0.0483334284
## you               0.1137422902 0.0967948604 0.077629528 0.1047163932
## credit            0.0429706584 0.0331942307 0.026848323 0.0331762069
## your              0.0898403129 0.0721281245 0.044352938 0.0922209908
## font              0.0279532394 0.0215169814 0.017647218 0.0212091289
## num000            0.0641153823 0.0519451665 0.043037297 0.0519365929
## money             0.0452744552 0.0345520739 0.028422685 0.0359594025
## hp                0.4309240379 0.3741331777 0.358241063 0.0095937503
## hpl               0.4027191933 0.3887567954 0.374376711 0.0018412535
## george            0.0481055122 0.0603270857 0.082421852 0.0229736101
## num650            0.6129209045 0.6022617104 0.584175561 0.0201340086
## lab               0.3802080976 0.4351240722 0.489207043 0.0018775677
## labs              0.0000000000 0.7003551741 0.685577722 0.0263549943
## telnet            0.7003551741 0.0000000000 0.821359071 0.0147328848
## num857            0.6855777224 0.8213590712 0.000000000 0.0207080668
## data              0.0263549943 0.0147328848 0.020708067 0.0000000000
## num415            0.6827440464 0.8182559390 0.995243691 0.0212362281
## num85             0.5411178800 0.5584091539 0.535508170 0.0198984011
## technology        0.6503199519 0.7485831090 0.725140647 0.0130505820
## num1999           0.0521070128 0.0441096346 0.035230686 0.0679300740
## parts             0.0029586865 0.0086575068 0.006962267 0.0403265890
## pm                0.0470363863 0.0650041530 0.060056550 0.1118743844
## direct            0.6335297031 0.7802060335 0.858955399 0.0224395541
## cs                0.0505548142 0.0127663631 0.008962767 0.0011675726
## meeting           0.0257586725 0.0209538822 0.015356275 0.0099167637
## original          0.0682220281 0.0889208937 0.114066622 0.0108741134
## project           0.0011073061 0.1108446139 0.007764925 0.0365613627
## re                0.0134558067 0.0066917646 0.018985929 0.0003559938
## edu               0.0083317752 0.0252021114 0.017992532 0.0175905063
## table             0.0033736461 0.0009797627 0.002517480 0.0031672709
## conference        0.0003846002 0.0133367042 0.009989861 0.0069608619
## charSemicolon     0.0224497251 0.0169146542 0.009312327 0.0064081734
## charRoundbracket  0.2277163615 0.2558814424 0.298967625 0.0188809980
## charSquarebracket 0.0020717531 0.0046514682 0.012231067 0.0281770522
## charExclamation   0.0600628012 0.0458864132 0.039062809 0.0501867455
## charDollar        0.0680304013 0.0540539228 0.045826239 0.0523705980
## charHash          0.0745855364 0.0041019426 0.011551143 0.0084545929
## capitalAve        0.0155502474 0.0125336284 0.010592141 0.0162172097
## capitalLong       0.0343417473 0.0280973452 0.025362449 0.0254745700
## capitalTotal      0.0645956522 0.0518984681 0.049347676 0.0188148121
##                         num415       num85  technology     num1999        parts
## make              0.0285884545 0.044842007 0.056882835 0.052744183 6.605356e-03
## address           0.0134429884 0.027043742 0.032238583 0.028983211 8.109559e-03
## all               0.0618751395 0.038328829 0.040633102 0.067123679 4.599206e-03
## num3d             0.0069219127 0.005811544 0.006734026 0.007657471 2.661989e-03
## our               0.0278986390 0.049436261 0.059609413 0.078170335 1.699240e-01
## over              0.0362169991 0.051543217 0.054679122 0.055360648 1.563951e-02
## remove            0.0408604348 0.052444862 0.054688722 0.049418001 1.484748e-02
## internet          0.0347137317 0.033050993 0.031817937 0.020826928 1.172802e-02
## order             0.0313289271 0.040981497 0.054886735 0.040251267 6.728179e-03
## mail              0.0103468095 0.015522050 0.020134467 0.004232605 1.539843e-02
## receive           0.0366481191 0.046182680 0.050903960 0.036624325 8.194087e-03
## will              0.0524307545 0.043401976 0.010979056 0.045194093 2.227936e-02
## people            0.0310626737 0.047721516 0.047398260 0.035156028 1.282222e-02
## report            0.0166239733 0.022061895 0.001030677 0.029770500 3.276360e-03
## addresses         0.0228858667 0.024458032 0.034527898 0.042023474 1.162777e-02
## free              0.0397702863 0.053818954 0.059722867 0.062992881 1.440794e-02
## business          0.0412185077 0.052441298 0.034530411 0.046301858 1.448454e-02
## email             0.0433019960 0.008290727 0.015384285 0.048193156 1.295831e-02
## you               0.0777532347 0.088840394 0.132221246 0.124637560 2.793223e-02
## credit            0.0278312351 0.034976818 0.043115904 0.046785730 2.567752e-02
## your              0.0450803479 0.082170020 0.107153430 0.115663508 1.835211e-02
## font              0.0178929841 0.023606461 0.028190245 0.034948357 4.000192e-03
## num000            0.0432501741 0.052658259 0.065586677 0.071380314 1.733035e-02
## money             0.0291410322 0.036492134 0.045627340 0.054245891 5.506620e-03
## hp                0.3567309208 0.285562800 0.378535647 0.123907971 2.011026e-02
## hpl               0.3732709127 0.326746219 0.355187043 0.179212795 4.636881e-02
## george            0.0816868077 0.033164228 0.039157712 0.016121324 1.168204e-02
## num650            0.5820702235 0.568367428 0.572498951 0.024354731 1.225438e-02
## lab               0.4871639072 0.305995466 0.391055830 0.007269186 5.330146e-03
## labs              0.6827440464 0.541117880 0.650319952 0.052107013 2.958686e-03
## telnet            0.8182559390 0.558409154 0.748583109 0.044109635 8.657507e-03
## num857            0.9952436910 0.535508170 0.725140647 0.035230686 6.962267e-03
## data              0.0212362281 0.019898401 0.013050582 0.067930074 4.032659e-02
## num415            0.0000000000 0.533526692 0.722065301 0.036549101 7.091054e-03
## num85             0.5335266915 0.000000000 0.495539522 0.023387566 1.031296e-02
## technology        0.7220653007 0.495539522 0.000000000 0.061924965 9.198663e-03
## num1999           0.0365491008 0.023387566 0.061924965 0.000000000 4.921353e-03
## parts             0.0070910544 0.010312964 0.009198663 0.004921353 0.000000e+00
## pm                0.0593567301 0.030868106 0.083897357 0.227401319 1.108923e-02
## direct            0.8557210878 0.501730812 0.680027624 0.019550904 9.355460e-03
## cs                0.0092469858 0.029354370 0.019031031 0.103009098 5.963977e-03
## meeting           0.0157519335 0.033293906 0.030364748 0.009304534 1.635511e-01
## original          0.1131678750 0.056445431 0.074441397 0.324067574 9.939269e-03
## project           0.0073893003 0.004186908 0.010334938 0.003206279 2.597548e-03
## re                0.0184659723 0.015737941 0.010242306 0.069512560 7.209994e-05
## edu               0.0183766771 0.010524491 0.034135828 0.134073003 8.883419e-03
## table             0.0023210350 0.020267961 0.001579537 0.019051380 3.971741e-03
## conference        0.0103881876 0.008109436 0.022533019 0.063365119 3.317312e-04
## charSemicolon     0.0097943769 0.020629535 0.019700900 0.044604461 1.501609e-02
## charRoundbracket  0.2976188432 0.186459752 0.237292687 0.083196174 3.154710e-03
## charSquarebracket 0.0121592957 0.033012511 0.005916613 0.062811444 6.730204e-03
## charExclamation   0.0362324154 0.045258775 0.057132828 0.054093189 1.190002e-02
## charDollar        0.0416779551 0.047697175 0.060309083 0.069756101 1.177313e-02
## charHash          0.0114320329 0.010446006 0.013483146 0.026258659 2.593916e-03
## capitalAve        0.0008320091 0.013181998 0.019483355 0.014682745 5.203977e-03
## capitalLong       0.0217847983 0.026441899 0.035789542 0.032997789 6.170952e-03
## capitalTotal      0.0473999134 0.043872780 0.050404271 0.002666160 9.468409e-03
##                             pm      direct           cs      meeting
## make              0.0040816927 0.033953710 0.0192015997 0.0226410902
## address           0.0211309184 0.018761386 0.0141981918 0.0245638854
## all               0.0194705651 0.051719521 0.0333739350 0.0188449582
## num3d             0.0048502546 0.007577681 0.0059309835 0.0084330703
## our               0.0457887123 0.023081675 0.0478181299 0.1080802129
## over              0.0494067688 0.028423658 0.0272632448 0.0543487050
## remove            0.0543603240 0.030267384 0.0336627388 0.0508567161
## internet          0.0313049813 0.003989796 0.0140612026 0.0447660924
## order             0.0446147162 0.004748995 0.0348773559 0.0493487788
## mail              0.0153102187 0.010640743 0.0295857132 0.0540521268
## receive           0.0502364719 0.022238307 0.0343143534 0.0460752817
## will              0.0180612980 0.035498256 0.0352175004 0.0897235215
## people            0.0229453378 0.009762093 0.0176864432 0.0419435737
## report            0.0268364638 0.021561331 0.0208261136 0.0024653224
## addresses         0.0127013497 0.053331544 0.0118153462 0.0333174229
## free              0.0455115543 0.032566834 0.0317903075 0.0342947243
## business          0.0447228519 0.003564518 0.0353917952 0.0400009845
## email             0.0226940725 0.005289105 0.0313917423 0.0521258351
## you               0.0394986529 0.059102024 0.0600787151 0.0895906246
## credit            0.0361128610 0.001162255 0.0239204764 0.0338406767
## your              0.0709495913 0.015045202 0.0606401977 0.0894939014
## font              0.0233735382 0.022139046 0.0152391153 0.0216630626
## num000            0.0395923803 0.001973227 0.0369195586 0.0525670993
## money             0.0367560668 0.025138965 0.0252129303 0.0351486340
## hp                0.0687685115 0.322499214 0.0055684926 0.0096678348
## hpl               0.0783548625 0.335954047 0.0208857954 0.0579501529
## george            0.0005318936 0.062645644 0.0165949403 0.0009518897
## num650            0.0617611105 0.541601990 0.0319102566 0.0061677625
## lab               0.0121951568 0.454287540 0.0158511314 0.4243153154
## labs              0.0470363863 0.633529703 0.0505548142 0.0257586725
## telnet            0.0650041530 0.780206033 0.0127663631 0.0209538822
## num857            0.0600565502 0.858955399 0.0089627666 0.0153562746
## data              0.1118743844 0.022439554 0.0011675726 0.0099167637
## num415            0.0593567301 0.855721088 0.0092469858 0.0157519335
## num85             0.0308681062 0.501730812 0.0293543702 0.0332939061
## technology        0.0838973566 0.680027624 0.0190310305 0.0303647484
## num1999           0.2274013195 0.019550904 0.1030090984 0.0093045336
## parts             0.0110892296 0.009355460 0.0059639774 0.1635511427
## pm                0.0000000000 0.036086514 0.0256373931 0.0448745320
## direct            0.0360865137 0.000000000 0.0141433062 0.0238322292
## cs                0.0256373931 0.014143306 0.0000000000 0.0151483426
## meeting           0.0448745320 0.023832229 0.0151483426 0.0000000000
## original          0.2632837667 0.093435682 0.0728193544 0.0119492444
## project           0.0209893355 0.001890946 0.0099125772 0.0023167797
## re                0.0640284273 0.005897540 0.0064057172 0.0068315640
## edu               0.0004889192 0.026015269 0.3583793773 0.0183797421
## table             0.0075806680 0.002780664 0.0074230299 0.0125185138
## conference        0.0170322707 0.014002270 0.0006365934 0.0008906059
## charSemicolon     0.0228247691 0.018721284 0.0625895130 0.0075568505
## charRoundbracket  0.0671579819 0.263205815 0.0153654334 0.0204105492
## charSquarebracket 0.0476572897 0.010051389 0.0285984529 0.0129531557
## charExclamation   0.0204535162 0.029393359 0.0249844688 0.0373087564
## charDollar        0.0489761908 0.016774625 0.0392765652 0.0503858909
## charHash          0.0115498247 0.009841183 0.0124044275 0.0025993697
## capitalAve        0.0153536804 0.006670768 0.0087762912 0.0179702202
## capitalLong       0.0297621970 0.007249799 0.0223133309 0.0331226474
## capitalTotal      0.0556118764 0.029322378 0.0313670906 0.0623956662
##                      original      project           re          edu
## make              0.021261794 2.178379e-02 3.226205e-02 0.0465927300
## address           0.012887794 2.018649e-02 1.292346e-02 0.0219663668
## all               0.046105743 5.749077e-02 4.969854e-02 0.0576124275
## num3d             0.009870291 6.332086e-03 1.372137e-02 0.0095447133
## our               0.051327754 1.323619e-02 5.474229e-02 0.0780280933
## over              0.033481229 2.957178e-02 4.849358e-02 0.0290752224
## remove            0.050071354 3.560921e-02 4.773508e-02 0.0572739847
## internet          0.002455485 3.221428e-02 1.181064e-02 0.0425735184
## order             0.037385498 3.553827e-02 7.341934e-02 0.0563128056
## mail              0.023775722 2.887309e-02 2.441671e-02 0.0353694095
## receive           0.037921655 3.710464e-02 6.063890e-02 0.0513169082
## will              0.029392153 9.005748e-03 7.760695e-02 0.0706261291
## people            0.008432761 2.622451e-02 4.801773e-02 0.0201486945
## report            0.001391581 1.206949e-02 5.399290e-03 0.0200793185
## addresses         0.037918334 1.814736e-02 3.641921e-02 0.0254153346
## free              0.045552881 3.145570e-02 4.221784e-02 0.0488289201
## business          0.050457931 2.436085e-02 5.702988e-02 0.0564664014
## email             0.016862922 3.373252e-02 5.058725e-02 0.0395801557
## you               0.049123067 6.470333e-02 1.342495e-01 0.0193717564
## credit            0.033013341 1.492542e-02 5.004538e-02 0.0356502987
## your              0.048422841 6.002285e-02 3.842438e-02 0.0796639568
## font              0.022401127 1.249552e-02 3.333617e-02 0.0216702510
## num000            0.046161090 3.680699e-02 5.641104e-02 0.0571982954
## money             0.038459364 2.330031e-02 4.707655e-02 0.0303988081
## hp                0.095270531 3.021006e-04 5.783591e-02 0.0452423719
## hpl               0.124361546 1.815585e-02 3.020758e-03 0.0375131772
## george            0.011834864 1.369224e-02 1.108269e-03 0.0388828497
## num650            0.081544803 4.159053e-03 5.835609e-03 0.0030246874
## lab               0.045520385 2.266160e-03 1.042161e-02 0.0231407383
## labs              0.068222028 1.107306e-03 1.345581e-02 0.0083317752
## telnet            0.088920894 1.108446e-01 6.691765e-03 0.0252021114
## num857            0.114066622 7.764925e-03 1.898593e-02 0.0179925324
## data              0.010874113 3.656136e-02 3.559938e-04 0.0175905063
## num415            0.113167875 7.389300e-03 1.846597e-02 0.0183766771
## num85             0.056445431 4.186908e-03 1.573794e-02 0.0105244906
## technology        0.074441397 1.033494e-02 1.024231e-02 0.0341358279
## num1999           0.324067574 3.206279e-03 6.951256e-02 0.1340730027
## parts             0.009939269 2.597548e-03 7.209994e-05 0.0088834190
## pm                0.263283767 2.098934e-02 6.402843e-02 0.0004889192
## direct            0.093435682 1.890946e-03 5.897540e-03 0.0260152690
## cs                0.072819354 9.912577e-03 6.405717e-03 0.3583793773
## meeting           0.011949244 2.316780e-03 6.831564e-03 0.0183797421
## original          0.000000000 1.159858e-02 9.567863e-02 0.0081399905
## project           0.011598581 0.000000e+00 1.229474e-03 0.0170024042
## re                0.095678629 1.229474e-03 0.000000e+00 0.0398351728
## edu               0.008139990 1.700240e-02 3.983517e-02 0.0000000000
## table             0.021775680 3.339051e-03 1.193851e-02 0.0105072112
## conference        0.002640286 8.596095e-06 6.017755e-03 0.0151142803
## charSemicolon     0.020560658 6.015503e-03 2.303299e-02 0.0233417219
## charRoundbracket  0.059974529 7.411853e-03 2.491348e-03 0.0180110274
## charSquarebracket 0.096829387 1.090554e-02 2.932896e-03 0.0049985253
## charExclamation   0.046515412 3.174995e-02 5.477039e-02 0.0359995713
## charDollar        0.058976631 3.924899e-02 5.335491e-02 0.0527176180
## charHash          0.015813690 4.086810e-03 2.432517e-02 0.0154239069
## capitalAve        0.018006368 1.340468e-02 2.741841e-02 0.0173113035
## capitalLong       0.019363744 2.499261e-02 4.886893e-02 0.0315777230
## capitalTotal      0.040603565 4.449521e-02 1.002697e-01 0.0503289753
##                          table   conference charSemicolon charRoundbracket
## make              1.682853e-04 1.692827e-02   0.023449626      0.027096822
## address           9.709964e-03 1.460151e-02   0.004667391      0.044332185
## all               3.179064e-02 2.568483e-02   0.031405918      0.021928697
## num3d             3.564965e-03 1.068030e-03   0.003343485      0.010928852
## our               2.835892e-02 2.864497e-02   0.032311366      0.043127432
## over              1.409388e-02 3.109848e-02   0.024330392      0.002669307
## remove            1.880953e-02 3.168836e-02   0.034981046      0.046764497
## internet          1.105663e-02 2.165119e-02   0.029564174      0.028347606
## order             9.832825e-03 2.194160e-02   0.016484387      0.031089928
## mail              1.796832e-02 1.251542e-02   0.014346424      0.002322288
## receive           2.009403e-02 2.118151e-02   0.034470380      0.057802577
## will              5.269911e-03 2.747959e-02   0.030414906      0.034819391
## people            1.325945e-02 1.957206e-02   0.026641783      0.044720646
## report            5.175112e-02 1.504132e-02   0.019422668      0.001708036
## addresses         1.189611e-02 2.161836e-02   0.017148611      0.006227419
## free              1.898046e-02 2.612720e-02   0.028028954      0.041281177
## business          7.527992e-03 2.777412e-02   0.036755121      0.030050331
## email             2.642265e-02 3.039509e-02   0.040884295      0.035648846
## you               4.305611e-03 5.708895e-02   0.049059279      0.120076359
## credit            9.270122e-03 2.149944e-02   0.024959294      0.022689596
## your              1.813804e-02 4.815321e-02   0.059984600      0.076237209
## font              9.159848e-03 1.394118e-02   0.399378775      0.043697109
## num000            1.861102e-02 3.078800e-02   0.028201810      0.035515731
## money             1.147614e-02 1.731044e-02   0.017327020      0.029030237
## hp                3.416112e-03 7.878909e-03   0.036394060      0.136502537
## hpl               1.941274e-02 3.015458e-03   0.019216374      0.150143639
## george            9.691701e-03 1.135072e-02   0.025639552      0.029264755
## num650            7.988997e-03 1.020134e-02   0.023614441      0.289765958
## lab               1.704075e-03 1.558340e-03   0.019178061      0.146921423
## labs              3.373646e-03 3.846002e-04   0.022449725      0.227716362
## telnet            9.797627e-04 1.333670e-02   0.016914654      0.255881442
## num857            2.517480e-03 9.989861e-03   0.009312327      0.298967625
## data              3.167271e-03 6.960862e-03   0.006408173      0.018880998
## num415            2.321035e-03 1.038819e-02   0.009794377      0.297618843
## num85             2.026796e-02 8.109436e-03   0.020629535      0.186459752
## technology        1.579537e-03 2.253302e-02   0.019700900      0.237292687
## num1999           1.905138e-02 6.336512e-02   0.044604461      0.083196174
## parts             3.971741e-03 3.317312e-04   0.015016090      0.003154710
## pm                7.580668e-03 1.703227e-02   0.022824769      0.067157982
## direct            2.780664e-03 1.400227e-02   0.018721284      0.263205815
## cs                7.423030e-03 6.365934e-04   0.062589513      0.015365433
## meeting           1.251851e-02 8.906059e-04   0.007556851      0.020410549
## original          2.177568e-02 2.640286e-03   0.020560658      0.059974529
## project           3.339051e-03 8.596095e-06   0.006015503      0.007411853
## re                1.193851e-02 6.017755e-03   0.023032990      0.002491348
## edu               1.050721e-02 1.511428e-02   0.023341722      0.018011027
## table             0.000000e+00 6.205997e-03   0.001520502      0.001797937
## conference        6.205997e-03 0.000000e+00   0.002862612      0.010607209
## charSemicolon     1.520502e-03 2.862612e-03   0.000000000      0.059982418
## charRoundbracket  1.797937e-03 1.060721e-02   0.059982418      0.000000000
## charSquarebracket 3.734855e-03 8.107898e-03   0.009104759      0.021919083
## charExclamation   1.700925e-02 2.592801e-02   0.015300496      0.022042059
## charDollar        2.119594e-02 3.138020e-02   0.005217121      0.058225105
## charHash          3.417682e-05 1.020133e-02   0.059562708      0.038416073
## capitalAve        6.932980e-03 7.180517e-03   0.004409971      0.044615793
## capitalLong       1.026303e-02 1.510052e-02   0.049957164      0.431296288
## capitalTotal      9.816706e-04 6.490121e-03   0.070785879      0.157199305
##                   charSquarebracket charExclamation  charDollar     charHash
## make                   3.209511e-02     0.053719412 0.090493681 6.957253e-03
## address                1.914401e-02     0.010047941 0.004906670 5.652416e-03
## all                    2.538078e-02     0.097721623 0.083173895 1.420531e-02
## num3d                  6.962042e-03     0.002271545 0.016427126 2.460491e-03
## our                    2.512953e-02     0.022652501 0.051387610 8.578909e-03
## over                   2.525279e-02     0.050127304 0.116330947 7.345910e-04
## remove                 2.666380e-02     0.052732146 0.077013442 4.958380e-02
## internet               1.740288e-02     0.032029857 0.068971303 8.571457e-03
## order                  5.044004e-03     0.036990272 0.160183404 1.006670e-04
## mail                   2.322363e-04     0.025574843 0.064298896 4.700325e-02
## receive                2.972814e-02     0.024833733 0.074915892 5.154212e-03
## will                   4.455737e-02     0.007914177 0.019137779 2.937600e-02
## people                 2.733847e-02     0.043138964 0.188727334 1.469677e-02
## report                 1.195500e-02     0.010675041 0.084370785 5.624260e-03
## addresses              9.863468e-03     0.009720701 0.120663334 3.606488e-03
## free                   2.843119e-02     0.101384013 0.030032971 3.713804e-02
## business               3.351204e-02     0.069930532 0.106528945 3.104082e-03
## email                  2.223230e-02     0.042878940 0.077914958 3.060596e-02
## you                    6.129867e-02     0.155144473 0.093578911 3.496881e-03
## credit                 1.168519e-02     0.057577450 0.053215397 1.247774e-02
## your                   5.417629e-02     0.071457165 0.158340476 4.700013e-03
## font                   4.303239e-05     0.004815566 0.007545806 1.998387e-01
## num000                 2.912343e-02     0.067371022 0.330162221 1.317493e-02
## money                  2.101517e-02     0.046251598 0.089143850 1.303144e-04
## hp                     3.416152e-02     0.085773245 0.090358020 4.958737e-02
## hpl                    6.697365e-02     0.081665090 0.087225900 2.191583e-02
## george                 1.642894e-02     0.063983994 0.072911912 2.167426e-02
## num650                 3.534754e-02     0.059859369 0.061774374 1.156290e-02
## lab                    2.796885e-03     0.040759731 0.053702088 4.719951e-03
## labs                   2.071753e-03     0.060062801 0.068030401 7.458554e-02
## telnet                 4.651468e-03     0.045886413 0.054053923 4.101943e-03
## num857                 1.223107e-02     0.039062809 0.045826239 1.155114e-02
## data                   2.817705e-02     0.050186746 0.052370598 8.454593e-03
## num415                 1.215930e-02     0.036232415 0.041677955 1.143203e-02
## num85                  3.301251e-02     0.045258775 0.047697175 1.044601e-02
## technology             5.916613e-03     0.057132828 0.060309083 1.348315e-02
## num1999                6.281144e-02     0.054093189 0.069756101 2.625866e-02
## parts                  6.730204e-03     0.011900021 0.011773125 2.593916e-03
## pm                     4.765729e-02     0.020453516 0.048976191 1.154982e-02
## direct                 1.005139e-02     0.029393359 0.016774625 9.841183e-03
## cs                     2.859845e-02     0.024984469 0.039276565 1.240443e-02
## meeting                1.295316e-02     0.037308756 0.050385891 2.599370e-03
## original               9.682939e-02     0.046515412 0.058976631 1.581369e-02
## project                1.090554e-02     0.031749948 0.039248992 4.086810e-03
## re                     2.932896e-03     0.054770386 0.053354907 2.432517e-02
## edu                    4.998525e-03     0.035999571 0.052717618 1.542391e-02
## table                  3.734855e-03     0.017009248 0.021195936 3.417682e-05
## conference             8.107898e-03     0.025928007 0.031380198 1.020133e-02
## charSemicolon          9.104759e-03     0.015300496 0.005217121 5.956271e-02
## charRoundbracket       2.191908e-02     0.022042059 0.058225105 3.841607e-02
## charSquarebracket      0.000000e+00     0.029249363 0.030682669 5.886359e-03
## charExclamation        2.924936e-02     0.000000000 0.129167245 2.109711e-02
## charDollar             3.068267e-02     0.129167245 0.000000000 1.579964e-02
## charHash               5.886359e-03     0.021097106 0.015799638 0.000000e+00
## capitalAve             1.001505e-02     0.046707513 0.094993968 1.660079e-02
## capitalLong            1.784020e-02     0.067158834 0.203780803 7.549290e-02
## capitalTotal           1.383735e-03     0.038068123 0.230750294 6.003455e-02
##                     capitalAve  capitalLong capitalTotal
## make              0.0435220815 0.0549154680 0.0912654141
## address           0.0038561821 0.0023229052 0.0176072315
## all               0.0873688246 0.0931700634 0.0690902903
## num3d             0.0028276695 0.0165835615 0.0184738663
## our               0.0489703385 0.0433780635 0.0018717405
## over              0.0126508309 0.0669041663 0.0710082419
## remove            0.0421621344 0.0581702001 0.0030600818
## internet          0.0077655997 0.0318767972 0.0451350912
## order             0.1096683264 0.1669528786 0.2634103322
## mail              0.0614440165 0.0825353125 0.0889325803
## receive           0.0275166866 0.0784043294 0.1188771510
## will              0.0135086050 0.0128193293 0.0196889740
## people            0.0135874328 0.0389571187 0.1155530710
## report            0.0008744141 0.0453058252 0.1702989353
## addresses         0.0095910319 0.1819834471 0.1631348647
## free              0.0169321721 0.0252672103 0.0012965090
## business          0.0389990569 0.0596109230 0.0758939608
## email             0.0094770032 0.0600549632 0.0430068764
## you               0.0319921946 0.0007916675 0.0084561133
## credit            0.0757798881 0.1122742280 0.1084402805
## your              0.0323717590 0.0640745644 0.0497352041
## font              0.0205445940 0.0301670487 0.1343887259
## num000            0.0062829747 0.1149809427 0.1862564899
## money             0.0066877024 0.0333474118 0.0738845041
## hp                0.0175432622 0.0466030161 0.0415675008
## hpl               0.0239283002 0.0475831506 0.0598796453
## george            0.0249796876 0.0505768235 0.1033581926
## num650            0.0126263783 0.0346223720 0.0701874473
## lab               0.0151735807 0.0328240715 0.0613901596
## labs              0.0155502474 0.0343417473 0.0645956522
## telnet            0.0125336284 0.0280973452 0.0518984681
## num857            0.0105921410 0.0253624492 0.0493476759
## data              0.0162172097 0.0254745700 0.0188148121
## num415            0.0008320091 0.0217847983 0.0473999134
## num85             0.0131819981 0.0264418995 0.0438727797
## technology        0.0194833553 0.0357895420 0.0504042712
## num1999           0.0146827447 0.0329977885 0.0026661605
## parts             0.0052039767 0.0061709524 0.0094684095
## pm                0.0153536804 0.0297621970 0.0556118764
## direct            0.0066707680 0.0072497989 0.0293223782
## cs                0.0087762912 0.0223133309 0.0313670906
## meeting           0.0179702202 0.0331226474 0.0623956662
## original          0.0180063679 0.0193637445 0.0406035650
## project           0.0134046792 0.0249926102 0.0444952071
## re                0.0274184077 0.0488689285 0.1002696847
## edu               0.0173113035 0.0315777230 0.0503289753
## table             0.0069329800 0.0102630288 0.0009816706
## conference        0.0071805167 0.0151005224 0.0064901207
## charSemicolon     0.0044099706 0.0499571637 0.0707858785
## charRoundbracket  0.0446157934 0.4312962875 0.1571993054
## charSquarebracket 0.0100150514 0.0178402010 0.0013837348
## charExclamation   0.0467075133 0.0671588336 0.0380681232
## charDollar        0.0949939676 0.2037808031 0.2307502939
## charHash          0.0166007850 0.0754929024 0.0600345524
## capitalAve        0.0000000000 0.4859902008 0.1880284801
## capitalLong       0.4859902008 0.0000000000 0.5346867746
## capitalTotal      0.1880284801 0.5346867746 0.0000000000

which(M > 0.8, arr.ind=T)

##        row col
## num857  32  31
## num415  34  31
## telnet  31  32
## num415  34  32
## direct  40  32
## telnet  31  34
## num857  32  34
## direct  40  34
## num857  32  40
## num415  34  40

Basic PCA idea * We might not need every predictor * a weighted combination of predictors might be better * We should pick this cobination to capture the “most information” possible * benefits + reduced number of predictors + reduced noise (due to averaging)

You have multipvaraite variables, * find a new set of multivariate variables that are uncorrelated and explain as much variance as possible. * if you put all the variables together in one matrix, find the best matrix created with fewer variables that explains the orginal data.

Correlated predictors

library(caret); library(kernlab); data(spam)
inTrain <- createDataPartition(y=spam$type, p=0.75, list=FALSE)

training <- spam[inTrain,]
testing <- spam[-inTrain,]


M <- abs(cor(training[,-58]))
diag(M) <- 0
which(M > 0.8, arr.ind = T)

##        row col
## num415  34  32
## direct  40  32
## num857  32  34
## direct  40  34
## num857  32  40
## num415  34  40

names(spam)[c(34,32)]

## [1] "num415" "num857"

plot(spam[,34],spam[,32])

# We could rotate the plot
x <- 0.71 * training$num415 + 0.71* training$num857
y <- 0.71 * training$num415 - 0.71* training$num857


plot(x,y)

# the sum capture more information than subtraction

Related Problems

You have multivariate variables X1, …, Xn, so X11,….X1m * Find a new set of multivariate variables that are uncorrelated and explain as much variance as possible.

• If you put all the variables together in one matrix, find the best matrix created with fewer variables that explains the original data.

The first goal is statistical and the second goal is data compression.

Related solutions - PCA/ SVD

SVD if X is a matrix with each variable in a column and each observation in a row then the SVD is a “matrix decomposition”

X=UDV^T

where the columns of U are orthogonal (left singular vectors), the columns of V are orthogonal (right singluar vectors), and D is a diagonal matrix (singular values)

PCA The principal components are equal to the right singular values if you first scale (subtract the mean, divide by the standard deviation) the variables.

Principal components in R - prcomp

library(caret); library(kernlab); data(spam)
smallSpam <- spam[,c(34,32)]
prComp <- prcomp(smallSpam)
plot(prComp$x[,1],prComp$x[,2])

prComp$rotation # get the rotation matrx, how it summing up each component.

##              PC1        PC2
## num415 0.7080625  0.7061498
## num857 0.7061498 -0.7080625

# PCA on SPAM data
library(caret); library(kernlab); data(spam)
typeColor <- ((spam$stype=="spam")*1+1) #spam is red?
preProc <- preProcess(log10(spam[,-58]+1), method="pca", pcaComp=2)
spamPC <- predict(preProc, log10(spam[,-58]+1))
plot(spamPC[,1],spamPC[,2],color=typeColor)

## Warning in plot.window(...): "color" is not a graphical parameter

## Warning in plot.xy(xy, type, ...): "color" is not a graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "color" is not a
## graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "color" is not a
## graphical parameter

## Warning in box(...): "color" is not a graphical parameter

## Warning in title(...): "color" is not a graphical parameter

# Preprocessing with PCA
library(caret); library(kernlab); data(spam)
inTrain <- createDataPartition(y=spam$type, p=0.75, list=FALSE)

training <- spam[inTrain,]
testing <- spam[-inTrain,]
preProc <- preProcess(log10(training[,-58]+1), method="pca", pcaComp=2)
trainPC <- predict(preProc, log10(training[,-58]+1))
# modelFit <- train(training$type ~., method="glm", data=trainPC)
# 
# testPC <- predict(preProc, log(testing[,-58]+1))
# 
# confusionMatrix(testing$type, predict(modelFit, testPC))

# Alternative
# modelFit <- train(training$type ~., method="glm", preProcess="pca", data=training)
# confusionMatrix(testing$type, predict(modelFit, testing))

Final thoughts on PCs

• Most useful for linear- type models
• can make it harder to interpret predictors
• watch out for outliers
  • transform first (with logs/ Box Cox)
  • plot predictors to identify problems
• For more info see exploratory data analysis

Week 8.3 Predictin with trees, Random Forests, & Model Based predicitons

Predicting with trees

Key ideas * iteratively split variables into groups * evaluate “homogeneity” within each group * split again if necessary

Pros: * Easy to interpret * Better performance in nonlinear settings

Cons: * Without pruning/ cross-validation can lead to overfitting * Harder to estimate uncertainty * Results may be variable

Basic Algorithm

• start with all varaibles in one group
• Find the vvariable/split that best separates the outcomes
• divide the data into two groups (“leaves”) on that split (“node)
• whithin each split, find the best variable/split that separates the outcomes
• continue until the groups are too small or sufficiently “pure”

measures of impurity 1. misclassification error 2. gini index

• 0 = perfect puity
• 0.5 = no purity

3. Deviance/ information gain

• 0= perfect purity
• 1= no purity

# Example : iris data
data(iris); library(ggplot2)
names(iris)

## [1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width"  "Species"

table(iris$Species)

## 
##     setosa versicolor  virginica 
##         50         50         50

inTrain <- createDataPartition(y=iris$Species, p=0.7, list=F)
training <- iris[inTrain,]
testing <- iris[-inTrain,]
dim(training);dim(testing)

## [1] 105   5

## [1] 45  5

# qplot(Petal.Width, Sepal.Width, colour=Species, data=training)

library(caret)
modFit <- train(Species ~., method="rpart", data=training)

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

print(modFit$finalModel) # tell me what all the node are and how they split

## n= 105 
## 
## node), split, n, loss, yval, (yprob)
##       * denotes terminal node
## 
## 1) root 105 70 setosa (0.3333333 0.3333333 0.3333333)  
##   2) Petal.Length< 2.5 35  0 setosa (1.0000000 0.0000000 0.0000000) *
##   3) Petal.Length>=2.5 70 35 versicolor (0.0000000 0.5000000 0.5000000)  
##     6) Petal.Width< 1.75 40  5 versicolor (0.0000000 0.8750000 0.1250000) *
##     7) Petal.Width>=1.75 30  0 virginica (0.0000000 0.0000000 1.0000000) *

# plot tree
plot(modFit$finalModel, uniform=T, main="Classification Tree") 
text(modFit$finalModel, use.n=T, all=T, cex=.8)

# Prettier plots
# install.packages("rattle")
library(rattle)

## Loading required package: tibble

## Loading required package: bitops

## debugging in: ls(env, pattern = p, all.names = TRUE)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##     length(grep("]", pattern, fixed = TRUE))) {
##     if (pattern == "[") {
##         pattern <- "\\["
##         warning("replaced regular expression pattern '[' by  '\\\\['")
##     }
##     else if (length(grep("[^\\\\]\\[<-", pattern))) {
##         pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##         warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##     }
## }
## debug: grep(pattern, all.names, value = TRUE)
## exiting from: ls(env, pattern = p, all.names = TRUE)

## Rattle: A free graphical interface for data science with R.
## Version 5.5.1 Copyright (c) 2006-2021 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.

fancyRpartPlot(modFit$finalModel)

# Predicting new values
predict(modFit, newdata=testing)

##  [1] setosa     setosa     setosa     setosa     setosa     setosa    
##  [7] setosa     setosa     setosa     setosa     setosa     setosa    
## [13] setosa     setosa     setosa     versicolor versicolor versicolor
## [19] versicolor virginica  versicolor versicolor versicolor versicolor
## [25] versicolor versicolor versicolor versicolor versicolor versicolor
## [31] virginica  virginica  virginica  virginica  virginica  virginica 
## [37] virginica  virginica  virginica  virginica  virginica  virginica 
## [43] virginica  virginica  virginica 
## Levels: setosa versicolor virginica

Notes and further resources * Classification trees are non-linear models + They use interactions between variables + Data transformations may be less important (monotone transformations ) + trees can also be used for regression problems (continuous outcome) * Note that three are multiple tree building options in R both in the caret package - party ,rpart and out of the caret package - tree

Bagging

Bootstrap aggregating (bagging)

Basic idea : 1. Resample cases and recalculate predictions 2. Average or majority vote

Notes: 1. similar bias 2. Reduced varaince 3. More useful for non-linear functions

Bagging is most useful for nonlinear models

Random Forests

1. Bootstrap samples
2. At each split, bootstrap variables
3. Grow ultiple trees and vote

Pros: Accuracy

Cons: speed interpretabiliyt overfitting

data(iris); library(ggplot2)

inTrain <- createDataPartition(y=iris$Species, p=0.7, list=F)
training <- iris[inTrain,]
testing <- iris[-inTrain,]

library(caret)
library(randomForest)

## randomForest 4.7-1.1

## Type rfNews() to see new features/changes/bug fixes.

## 
## Attaching package: 'randomForest'

## The following object is masked from 'package:rattle':
## 
##     importance

## The following object is masked from 'package:ggplot2':
## 
##     margin

## The following object is masked from 'package:dplyr':
## 
##     combine

modFit <- train ( Species ~., data=training, method="rf", prox=T)

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

modFit

## Random Forest 
## 
## 105 samples
##   4 predictor
##   3 classes: 'setosa', 'versicolor', 'virginica' 
## 
## No pre-processing
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 105, 105, 105, 105, 105, 105, ... 
## Resampling results across tuning parameters:
## 
##   mtry  Accuracy   Kappa    
##   2     0.9428762  0.9130450
##   3     0.9438762  0.9145208
##   4     0.9419160  0.9115092
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 3.

getTree(modFit$finalModel, k=2) # see the secon tree.

##    left daughter right daughter split var split point status prediction
## 1              2              3         3        2.70      1          0
## 2              0              0         0        0.00     -1          1
## 3              4              5         3        4.75      1          0
## 4              6              7         4        1.65      1          0
## 5              8              9         4        1.75      1          0
## 6              0              0         0        0.00     -1          2
## 7              0              0         0        0.00     -1          3
## 8             10             11         4        1.55      1          0
## 9              0              0         0        0.00     -1          3
## 10             0              0         0        0.00     -1          3
## 11             0              0         0        0.00     -1          2

pred <- predict(modFit, testing)

Note random forest are usually one of the two top performing algorithms along with boosting in prediction contests. random forest are difficult to interpret but often very accurate care should be taken to avoid overfitting.

Boosting

Basic ideas 1. take lots of (possibly) weak predictors 2. Weight them and add them up 3. get a stronger predictor

ada boost

Boosting in R Boosting can be used wiht any subset of classifiers One Large subclass is gradient boosting R packages: gbm - boosting with trees. mboost - model based boosting ada - statistical boosting based on additive logistic regression gamBoost for boosting generalized additive models

Wage example

library(ISLR); data(Wage); library(ggplot2); library(caret);
Wage <- subset(Wage, select=-c(logwage))
inTrain <- createDataPartition(y=Wage$wage, p=0.7, list=F)
training <- Wage[inTrain,]
testing <- Wage[-inTrain,]

# Fit the model
modFit <- train(wage~., method="gbm", data=training, verbose=F)

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 14: region2. Middle Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 15: region3. East North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 16: region4. West North Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 17: region5. South Atlantic has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 18: region6. East South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 19: region7. West South Central has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 20: region8. Mountain has no variation.

## Warning in (function (x, y, offset = NULL, misc = NULL, distribution =
## "bernoulli", : variable 21: region9. Pacific has no variation.

print(modFit)

## Stochastic Gradient Boosting 
## 
## 2102 samples
##    9 predictor
## 
## No pre-processing
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 2102, 2102, 2102, 2102, 2102, 2102, ... 
## Resampling results across tuning parameters:
## 
##   interaction.depth  n.trees  RMSE      Rsquared   MAE     
##   1                   50      34.13574  0.3250466  23.48468
##   1                  100      33.55827  0.3364646  23.07470
##   1                  150      33.46319  0.3386295  23.05979
##   2                   50      33.52205  0.3391159  22.99846
##   2                  100      33.36828  0.3421410  22.98541
##   2                  150      33.37424  0.3422357  23.01802
##   3                   50      33.35803  0.3433466  22.89738
##   3                  100      33.36546  0.3425059  23.01313
##   3                  150      33.48957  0.3386288  23.17279
## 
## Tuning parameter 'shrinkage' was held constant at a value of 0.1
## 
## Tuning parameter 'n.minobsinnode' was held constant at a value of 10
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were n.trees = 50, interaction.depth =
##  3, shrinkage = 0.1 and n.minobsinnode = 10.

Model BASED prediciton

basic idea 1. assume the data follow a probabilistic model 2. use bayes’ theorem to identify optimal classifiers

Pros: can take advantage of structure of the data may be computationally convenient arereasonably accurate on real problems

cons: make additional assumptions about the data when the model is incorrect you may get reduced accuracy

A range of models use this approach linear discriminant analysis assumes … is multivariate gaussian with same covariances quadratic discrimant analysis assume .. is multivariate gaussian with different covariance model based prediciton assume more complicate version for the covariance matrix naive abyes assumes independence between features for model building.

data(iris); library(ggplot2)
names(iris)

## [1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width"  "Species"

table(iris$Species)

## 
##     setosa versicolor  virginica 
##         50         50         50

inTrain <- createDataPartition(y=iris$Species, p=0.7, list=F)
training <- iris[inTrain,]
testing <- iris[-inTrain,]

modlda = train(Species ~., data=training, method="lda")

## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

modnb=train(Species~., data=training, method="nb")

## debugging in: ls(env, pattern = p, all.names = TRUE)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##     length(grep("]", pattern, fixed = TRUE))) {
##     if (pattern == "[") {
##         pattern <- "\\["
##         warning("replaced regular expression pattern '[' by  '\\\\['")
##     }
##     else if (length(grep("[^\\\\]\\[<-", pattern))) {
##         pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##         warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##     }
## }
## debug: grep(pattern, all.names, value = TRUE)
## exiting from: ls(env, pattern = p, all.names = TRUE)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)
## debugging in: ls(vars, all.names = T)
## debug: {
##     if (!missing(name)) {
##         pos <- tryCatch(name, error = function(e) e)
##         if (inherits(pos, "error")) {
##             name <- substitute(name)
##             if (!is.character(name)) 
##                 name <- deparse(name)
##             warning(gettextf("%s converted to character string", 
##                 sQuote(name)), domain = NA)
##             pos <- name
##         }
##     }
##     all.names <- .Internal(ls(envir, all.names, sorted))
##     if (!missing(pattern)) {
##         if ((ll <- length(grep("[", pattern, fixed = TRUE))) && 
##             ll != length(grep("]", pattern, fixed = TRUE))) {
##             if (pattern == "[") {
##                 pattern <- "\\["
##                 warning("replaced regular expression pattern '[' by  '\\\\['")
##             }
##             else if (length(grep("[^\\\\]\\[<-", pattern))) {
##                 pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##                 warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##             }
##         }
##         grep(pattern, all.names, value = TRUE)
##     }
##     else all.names
## }
## debug: if (!missing(name)) {
##     pos <- tryCatch(name, error = function(e) e)
##     if (inherits(pos, "error")) {
##         name <- substitute(name)
##         if (!is.character(name)) 
##             name <- deparse(name)
##         warning(gettextf("%s converted to character string", 
##             sQuote(name)), domain = NA)
##         pos <- name
##     }
## }
## debug: pos <- tryCatch(name, error = function(e) e)
## debug: if (inherits(pos, "error")) {
##     name <- substitute(name)
##     if (!is.character(name)) 
##         name <- deparse(name)
##     warning(gettextf("%s converted to character string", sQuote(name)), 
##         domain = NA)
##     pos <- name
## }
## debug: all.names <- .Internal(ls(envir, all.names, sorted))
## debug: if (!missing(pattern)) {
##     if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != 
##         length(grep("]", pattern, fixed = TRUE))) {
##         if (pattern == "[") {
##             pattern <- "\\["
##             warning("replaced regular expression pattern '[' by  '\\\\['")
##         }
##         else if (length(grep("[^\\\\]\\[<-", pattern))) {
##             pattern <- sub("\\[<-", "\\\\\\[<-", pattern)
##             warning("replaced '[<-' by '\\\\[<-' in regular expression pattern")
##         }
##     }
##     grep(pattern, all.names, value = TRUE)
## } else all.names
## debug: all.names
## exiting from: ls(vars, all.names = T)

## Warning in FUN(X[[i]], ...): Numerical 0 probability for all classes with
## observation 15

plda=predict(modlda, testing)
pnb= predict(modnb,testing)

table(plda, pnb)

##             pnb
## plda         setosa versicolor virginica
##   setosa         15          0         0
##   versicolor      0         14         0
##   virginica       0          1        15

## Week 8.4 Regularized regression

regularized regression

Basic idea * Fit a regression model * Penalize ( or shrink) large coefficients

Pros: can help with the bias/variance tradeoff can help with model selection

Cons: May be computationally demanding on large data sets Does not perform as well as random forests and boosting

Combining predictors